Structure of Atoms
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Structure of Atoms...
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CHEMISTRY CLASS XI
UNIT - 2
CBSE-i
STRUCTURE OF ATOM TEACHERS' MANUAL CENTRAL BOARD OF SECONDARY EDUCATION Shiksha Kendra, 2, Community Centre, Preet Vihar, Delhi-110092 INDIA
Teachers’ Manual on
Structure of Atom Class XI
• Unit 2
Central Board of Secondary Education Shiksha Kendra, 2 Community Centre, Preet Vihar, Delhi-110092
T
he CBSE-International is grateful for permission to reproduce and/or translate copyright material used in this publication. The acknowledgements have been included wherever appropriate and sources from where the material may be taken are duly mentioned. In case any thing has been missed out, the Board will be pleased to rectify the error at the earliest possible opportunity. All Rights of these documents are reserved. No part of this publication may be reproduced, printed or transmitted in any form without the prior permission of the CBSE-i. This material is meant for the use of schools who are a part of the CBSE-International only.
Contents Preface.....................................................................................vi Acknowledgement..................................................................viii Syllabus Coverage....................................................................ix Learning Outcomes..................................................................x Lesson Plan Matrix.................................................................xii Cross-Curricular Links............................................................xv Pre-Requisites........................................................................xvi Mind–Map............................................................................xvii Teachers’ Notes...................................................................1–14 Student Worksheets.................................................................15 Crossword Puzzle....................................................................21 Rubrics of Assessment for Learning.......................................24 Common Misconceptions.......................................................27 Additional Resource Links......................................................28
Preface
E
ducation plays the most important role in acquiring professional and social skills and a positive attitude to face the challenges of life.Curriculum is a comprehensive plan of any educational programme. It is also one of the means of bringing about qualitative improvement in an educational system. The Curriculum initiated by Central Board of Secondary Education -International (CBSE-i) is a progressive step in making the educational content responsive to global needs. It signifies the emergence of a fresh thought process in imparting a curriculum which would restore the independence of the learner to pursue the learning process in harmony with the existing personal, social and cultural ethos. The CBSE introduced the CBSE-i curriculum as a pilot project in few schools situated outside India in 2010 in classes I and IX and extended the programme to classes II, VI and X in the session 2011-12. It is going to be introduced in classes III, VII and for Senior Secondary classes with class XI in the session 2012-13. The Senior Secondary stage of education decides the course of life of any student. At this stage it becomes extremely important for students to develop the right attitude, a willingness to learn and an understanding of the world around them to be able to take right decisions for their future. The senior secondary curriculum is expected to provide necessary base for the growth of knowledge and skills and thereby enhance a student’s potential to face the challenges of global competitiveness. The CBSE-i Senior Secondary Curriculum aims at developing desired professional, managerial and communication skills as per the requirement of the world of work. CBSE-i is for the current session offering curriculum in ten subjects i.e. Physics Chemistry, Biology, Accountancy, Business-Studies, Economics, Geography, ICT, English, Mathematics I and Mathematics II. Mathematics at two levels caters to the differing needs of students of pure sciences or commerce. The Curriculum has been designed to nurture multiple intelligences like linguistic or verbal intelligence, logical-mathematical intelligence, spatial intelligence, sports
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Unit 11: Structure of Atom
intelligence, musical intelligence, inter-personal intelligence and intra-personal intelligence. The Core skills are the most significant aspects of a learner's holistic growth and learning curve. The objective of this part of the core of curriculum is to scaffold the learning experiences and to relate tacit knowledge with formal knowledge. This involves trans-disciplinary linkages that would form the core of the learning process. Perspectives, SEWA (Social Empowerment through Work and Action), Life Skills and Research would be the constituents of this 'Core'. The CBSE-i Curriculum evolves by building on learning experiences inside the classroom over a period of time. The Board while addressing the issues of empowerment with the help of the schools' administering this system strongly recommends that practicing teachers become skilful and lifelong learners and also transfer their learning experiences to their peers through the interactive platforms provided by the Board. The success of this curriculum depends upon its effective implementation and it is expected that the teachers will make efforts to create better facilities, develop linkages with the world of work and foster conducive environment as per recommendations made in the curriculum document. I appreciate the effort of Dr. Sadhana Parashar, Director (Training), CBSE, Dr. Srijata Das, Education Officer, CBSE and their teams involved in the development of this document. The CBSE-i website enables all stakeholders to participate in this initiative through the discussion forums. Any further suggestions on improving the portal are always welcome.
Vineet Joshi Chairman, CBSE
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Unit 11: Structure of Atom
Acknowledgements Advisory Shri Vineet Joshi, Chairman, CBSE Dr. Sadhana Parashar, Director (Training), CBSE
Conceptual Framework Shri G. Balasubramanian, Former Director (Acad), CBSE Ms. Abha Adams, Consultant, Step-by-Step School, Noida Dr. Sadhana Parashar, Director (Training), CBSE
Ideators: Classes XI and XII Prof. A K Bakshi
Ms. P Rajeshwari
Dr. Niti Nandini Chatnani
Ms. Neeta Rastogi
Dr. N K Sehgal
Ms Gayatri Khanna
Dr. Anil K Bali
Dr. Anshu
Prof. Kapil Kapoor
Mrs. Anita Makkar
Dr. Preeti Tewari
Dr Rajesh Hassija
Ms. Renu Anand
Prof. Biswajit Nag
Dr. Deeksha Bajpai
Mr. Mukesh Kumar
Dr. Barkatullah Khan
Dr. Jacqueline Symss
Mr. S K Agarwala
Dr. Om Vikas
Ms. Avnita Bir
Ms. Usha Sharma
Material Production Groups: Classes XI and XII English: Ms Gayatri Khanna Ms Renu Anand Ms. P Rajeshwary Ms. Sandhya Awasthi Ms. Manna Barua Ms. Veena Bhasin Ms. Urmil Guliani Ms. Sudha Ravi Mr. Anil Kumar Ms. Vijaylaxmi Raman Ms. Neerada Suresh Ms. Himaal Handoo Chemistry: Dr. G S Sodhi Dr. Vimal Rarh Dr. Shalini Baxi Dr. Vinita Arora Dr. Vandana Soni Ms. Charu Maini Ms. Rashmi Sharma Ms. Kavita Kapoor
Biology: Dr. Ranjana Saxena Dr. Neeraja Sood Dr. P Chitralekha Ms. Mridula Arora Ms. Lucy Jad Ms. Priyanka Choudhury Ms. Prerna Gosain Ms. Malini Sridhar Physics: Dr. B. Biswal Ms. Namrata Alwadhi Mr. Dhirender Sharma Ms. Vandana Banga Mr. Vivek Mathematics: Dr. Sushil Kumar Mrs. Monica Talwar Mrs. Charu Dureja Mrs. Seema Juneja Dr. H L Bhatia Mrs Neeru Aggarwal Dr. Saroj Khanna Dr Sushma Bansal
Geography: Ms. K Jaya Dr. Preeti Tewari Ms. Rupa Das Ms. S Fazal Daoud Firdausi Ms. Neena Phogat Ms. Sujata Sharma Ms. Deepa Kapoor Ms. Bharti Malhotra Ms. Isha Kaushik Mr. Riyaz Khan Economics: Mr. S K Agarwala Ms. Ambika Gulati Ms. Nidhi Singh Ms. Malti Modi Ms. Sapna Das Ms. Ingur Agarwal Ms. Shankar Kulkarni Mr Sandeep Sethi
Accountancy: Mr. S S Sehrawat Dr. K Mohna Dr. Balbir Singh Mr. Bhupendra Kriplani Dr. Shipra Vaidya Mr. Sandeep Sethi Business Studies: Dr. S K Bhatia Ms. Meenu Ranjan Arora Mrs. Shegorika Mr. Sandeep Sethi Ms. Usha Sharma Ms. Komal Bhatia Ms. Ravisha Aggarwal ICT: Mr. Mukesh Kumar Ms. Nancy Sehgal Ms. Purvi Srivastava Ms. Gurpreet Kaur
Chief Co-ordinator: Dr. Srijata Das, EO Co-ordinators
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Ms. Sugandh Sharma, EO
Dr Rashmi Sethi, EO
Ms. S. Radha Mahalakshmi, EO
Ms. Madhuchhanda, RO (Inn)
Mr. Navin Maini, RO (Tech)
Ms. Neelima Sharma, Consultant (English)
Shri R. P. Sharma, Consultant (Science)
Shri Al Hilal Ahmed, AEO
Shri R.P Singh, AEO
Ms. Anjali Chhabra, AEO
Ms Reema Arora, Consultant (Chemistry)
Mr. Sanjay Sachdeva, SO
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Unit 11: Structure of Atom
Syllabus Coverage 2.1 Introduction to structure of atom 2.2 Atomic Models 2.2.1 Thomson Model 2.2.2 Rutherford Model 2.2.3 Bohr Model 2.2.4 Dual Behaviour 2.3 Quantum mechanical model 2.3.1 Concept of orbitals 2.3.2 Heisenberg’s uncertainty principle 2.3.3 Quantum numbers 2.4 Shapes of atomic orbitals 2.4.1 Shape of s, p and d orbitals 2.4.2 Node and nodal surface 2.4.3 Shielding effect 2.5 Rules for filling electrons in orbitals 2.5.1 Aufbau principle 2.5.2 Pauli’s exclusion principle 2.5.3 Hund’s rule
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2.5.4 Electronic configuration of atoms
2.5.5 Stability of completely filled and half-filled orbitals
Unit 11: Structure of Atom
Learning Outcomes At the end of this unit, students would be able to:
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Recall the existence of sub atomic particles namely electrons, protons and neutrons in an atom.
u
Know about the Thomson and Rutherford models of atom and list their limitations.
u
Recall the meaning of terms atomic number, mass number, isotopes and isobars.
u
Appreciate the developments which led to Bohr model.
u
Understand the characteristics of Bohr model as well as the causes of its failure.
u
Comprehend the Planck’s quantum theory and Black body radiation phenomenon.
u
Appreciate that radiation and matter show dual behaviour.
u
Solve problems based on De Broglie relation.
u
Understand the concept of quantization of electronic energy levels.
u
Distinguish between orbit and orbital.
u
State the Heisenberg’s uncertainty principle and solve problems based on the same.
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List the important features of quantum mechanical model.
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Designate an orbital by n, l and m quantum numbers.
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Recognize the various permissible values for each quantum number.
Unit 11: Structure of Atom
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Understand the origin of electron spin quantum number.
u
Plot the orbital wave functions for s, p and d orbitals.
u
Draw the probability density plots of s, p and d orbitals.
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Understand the terms: Node and Nodal surface.
u
Calculate the number of nodes for any given orbital.
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Arrange various orbitals in order of increasing energies and plot their energy level diagrams.
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Understand the concept of shielding and define effective nuclear charge.
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Understand and apply Aufbau principle.
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Understand the (n+l) rule.
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Predict order of energies of orbitals.
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State and apply Pauli’s exclusion principle as well as Hund’s rule of maximum multiplicity.
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Represent the electronic configuration for any given atom.
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Calculate the number of valence electrons for any given element.
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Recognize the causes of stability of completely filled and half-filled sub shells.
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Understand the concept of exchange pair formation and exchange energy.
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Comprehend the contribution of symmetrical distribution of electrons towards stability.
Unit 11: Structure of Atom
Lesson Plan Matrix Content
Steps to be followed Teacher’s Tip
A. Warm up
To get the students engaged with the Unit contents: • Ice breaker: conduct a learning activity. • Establish relevance of what has been learnt • Tell students what they should expect to cover in this unit Please refer to the Warm-Up section below for details. 2.1 Introduction In this introductory to structure topic, it is very of atom important to establish prior knowledge and lay down the expectations. It is also critical to get the students thinking in a structured, scientific manner. Start with the historical evolution of atomic structure and trace the brief history of the scientists involved Recapitulate the concepts like atomic number and mass. Student Activity 1 Student Worksheet 1 xii
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Unit 11: Structure of Atom
Student’s Tip You will be asked to participate in warm up activities conducted by the teacher. Participate actively and let your thoughts and beliefs be known openly.
Skill Developed Learning Skills: Recall, Contrast Distinguish, give examples (Comprehension), Demonstration (Application), Life Skills: adaptability, selforganization, selfefficacy, flexibility
Observe critically and understand the various milestones in the evolution of atomic structure. Get acquainted with the scientists involved with the development of the atomic structure.
Learning Skills: Recall, Description (memory), Distinguish, Infer, give examples (Comprehension), Construction, Demonstration (Application), Distinguishing, Breaking down Solve problems based (analysis) on atomic number and atomic mass Life Skills: adaptability, selforganization, dealing with uncertainty, flexibility
2.2 Atomic models
2.3 Quantum mechanical model
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• In this topic the • The students salient features should try and and drawbacks of understand the the various atomic central ideas of the models (Thomson, various models Rutherford and and theories put Bohr) is discussed. together in this • A brief look at the section. electromagnetic • The students theory , Planck’s should theory, blackbody comprehend the radiation and successes and photoelectric effect failure of each is also done attempt and how it • The concept of paved the way for spectra (adsorption development. and emission) is also undertaken Student Worksheet 2
• In this section the development of the quantum mechanical model is undertaken. • The link between duality and the development of quantum mechanics is explained • The difference between the classical approach and quantum approach is also undertaken • The various quantum numbers are introduced Student Activity 2 Student Worksheet 3
Unit 11: Structure of Atom
Learning Skills: Recall, Identification, Description (memory), Distinguish, Infer, give examples (Comprehension), Demonstration (Application), Distinguishing, Breaking down (Analysis), Compare and Contrast
Life Skills: adaptability, selforganization, dealing with uncertainty, flexibility • Students should try Learning Skills: and comprehend Recall, the quantum Identification, approach Description • The students (memory), Infer, should also give examples understand (Comprehension), the evolution Applies, Solves, of quantum Generalizes mechanics (Application) • Students should learn to understand the applications of quantum numbers
2.4 Shapes of atomic orbitals
2.5 Rules for filling electrons in orbitals
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• The concept of • Students should probability of clearly understand finding electron the difference in a given space is between the discussed. meanings of orbit • The various shapes and orbital of atomic orbitals is • The students discussed should also learn to Student Worksheet 4 draw and represent the different shapes on paper
Learning Skills: Recall, Identification (memory), Infer, give examples (Comprehension), Applies, Solves, Generalizes (Application)
• The various rules • The students (Pauli’s exclusion should be able to principle, Hund’s write the electronic rule of maximum configurations multiplicity and based on the given Aufbau Principle) rules is discussed. • The students • The configuration should be able to based on the give the quantum various rules is numbers of any written electron within the • The extra stability atom of half filled and • The students fully filled orbital’s should be able is discussed to modify the Student Worksheet 5 configuration of certain elements based on extra stability of half filled and fully filled orbitals
Learning Skills: Identification (memory), Infer, give examples (Comprehension), Applies, Solves, Generalizes (Application)
Unit 11: Structure of Atom
Life Skills: adaptability, self-organization, dealing with uncertainty, flexibility
Life Skills: adaptability, self-organization, dealing with uncertainty, flexibility
Cross Curricular Links The origin of life, the origin of the earth and the solar system and ultimately, the origin and development of the entire Universe comes from the building blocks. These are the ultimate, the very fundamental building blocks that emerged at the very origin of the universe, the big bang. So, in the end it should be realized that everything we can see in the universe, whether a star, a planet, sun, moon, cloud, mountain, tree, man… is all made out of two kinds of building blocks: quarks and electrons. The destruction caused due to atomic bombs and the peaceful use of atomic energy comes from the understanding of the atomic structure. An activity is suggested where Student groups should research and present on destruction caused by the nuclear bombs and a brief outline on how they work. After each group has had a turn presenting, allow time for students to give feedback on each other’s work and make content corrections on presentations before they are submitted for grading.
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Unit 11: Structure of Atom
Pre-Requisites Recall the following concepts already learnt in previous classes.
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An atom is divisible and consists of charged particles.
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The atom consists of subatomic particles.
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The negative subatomic particle is known as the electron. Electron is represented by ‘e-The mass of an electron is considered to be negligible and its charge is minus one.
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The positive subatomic particle is known as the proton. The proton is represented as ‘p+’. The mass of a proton is taken as one unit and its charge as plus one.
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The neutron is a subatomic particle with no charge and mass nearly equal to that of a proton. It is represented by ‘n’.
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The mass of an atom is given by the sum of masses of protons and neutrons present in the nucleus.
Unit 11: Structure of Atom
Mind-Map Structure of the Atom
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Unit 11: Structure of Atom
Teachers’ Notes 2.1 Introduction Prerequisites Help the students recall the following concepts already learnt in previous classes: • An atom is the smallest particle of the element that can exist independently and retain all its chemical properties. • A molecule is the smallest particle of an element or a compound capable of independent existence under ordinary conditions. It shows all the properties of the substance. • A chemical formula of a compound shows its constituent elements and the number of atoms of each combining element. • The chemical formula of a molecular compound is determined by the valency of each element.
Warm up activity 1. Ice-breaker:
(a) All matter consists of particles called atoms.
(b) Atoms cannot be divided using chemicals. They do consist of parts, which include protons, neutrons, and electrons, but an atom is a basic chemical building block of matter.
(c) Each electron has a negative electrical charge.
(d) Each proton has a positive electrical charge. The charge of a proton and an electron are equal in magnitude, yet opposite in sign. Electrons and protons are electrically attracted to each other.
(e) Each neutron is electrically neutral. In other words, neutrons do not have a charge and are not electrically attracted to either electrons or protons.
(f) Protons and neutrons are about the same size as each other and are much larger than electrons.
(g) The mass of a proton is essentially the same as that of a neutron. The mass of a proton is 1840 times greater than the mass of an electron.
(h) The nucleus of an atom contains protons and neutrons. The nucleus carries a positive electrical charge.
(i) Electrons move around outside the nucleus.
(j) Almost all of the mass of an atom is in its nucleus; almost all of the volume of an atom is occupied by electrons.
(k) The number of protons (also known as its atomic number) determines the element. Varying the number of neutrons results in isotopes. Varying the number of electrons results in ions. Isotopes and ions of an atom with a constant number of protons are all variations of a single element.
(l) The particles within an atom are bound together by powerful forces. In general, electrons are easier to add or remove from an atom than a proton or neutron. Chemical reactions largely involve atoms or groups of atoms and the interactions between their electrons.
What is the Importance of Atomic Structure? Some properties of solid materials depend on geometrical atomic arrangements and interactions among the atoms, which eventually are controlled by the subatomic structure of the materials. Therefore, we will learn about the subatomic structure, elctronic configurations, and major bondings holding the atoms together. For example: Carbon (pure) can exist as graphite and diamond. Graphite is soft and greasy feel to it, Diamond is the hardest known material. This difference is because of the type of interatomic bonding in graphite and diamond.
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Unit 11: Structure of Atom
Instructions for Teachers: Study the periodic table and let the students revise the symbols of the elements and their atomic number and masses of elements (atomic number 1-30). Divide the students into groups and quiz them on atomic numbers and atomic masses of various elements. Recall the existence of sub atomic particles namely electrons, protons and neutrons in an atom.
Student Activity 1 • Take the help of a demonstration. • Demonstrate the following activity. Concepts to Investigate: To give the students a basic idea about the structure of an atom; which comprises of a dense and heavy mass at the centre, known as nucleus. Problem: What is the probability that a dart (representing an electron) will hit the center of the target (representing the nucleus of the atom)? Materials required: 2 sheets of white paper, carbon paper, compass, tape, dart, poster board, pencil Procedure: 1. Obtain two pieces of blank white, 8 1/2” × 11” paper and draw a small but visible mark in the center of each of the papers. Hold the papers together toward the light and align the center marks exactly. 2. Around the center dot of one of the papers, which you will call the target paper, draw concentric circles having radii of 1 cm, 3 cm, 5 cm, 7 cm, and 9 cm. Number the areas of the target 1, 2, 3, 4, and 5 starting with number 1 at the center.
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Unit 11: Structure of Atom
3. Place a piece of poster board on the floor, and lay the target paper face up on top of it. Cover the target paper with a piece of carbon paper, carbon side down. Then place the second piece of white paper on top with the center mark facing up. Use tape to fasten the three layers of paper in place on the poster board and to secure the poster board to the floor. 4. Stand over the target paper and drop a dart 100 times from chest height, attempting to hit the center mark. 5. Remove the tape from the papers. Separate the white papers and the carbon paper. Tabulate and record the number of hits in each area of the target paper. H elp the students fill the table provided at the end of the activity by collecting the data that they obtain. M ake them draw conclusions. Relate the findings to the model of an atom.
Extension Another useful conclusion obtained from the alpha particle scattering experiment regarding the validity of Coulomb’s law is that the force exerted on the alpha particles due to the nucleus is inversely proportional to the square of the distance of the alpha particle from the nucleus. When the alpha particles pass away from the nucleus, they experience a small repulsive force and suffer a negligible deviation from their paths. But the particles passing close to the nucleus experience a very high repulsive force and are scattered through a large angle. On the basis of Coulomb’s law, he also calculated the number (N) of alpha particles scattered at different angles, q and found the 1 following relationship: N ∝ 4 sin (q/2) 4
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Unit 11: Structure of Atom
This confirms that the scattering of alpha particles by the nucleus is in accordance with Coulomb’s law and is valid for atomic distances also. Rutherford’s experiment also gives information about the positive charge present in the nucleus of different metals. Rutherford bombarded alpha particles on the foils of various metals and detected the number of alpha particles scattered in a definite direction in the case of each metal. This number was found to be different for different metals. This shows that the positive charge present in the nucleus of different metals is different. Higher the positive charge in a nucleus, higher will be the repulsive force exerted by it on the alpha particle. Therefore, the angle of scattering of the alpha particle will be proportionately larger. Rutherford proved that the number of alpha particles scattered within a certain angular range by a metal is directly proportional to the square of the magnitude of the positive charge in the nucleus of that metal. On this basis, Chadwick found the positive charge present in the nucleus of different metals and came to the conclusion that the positive charge in the nucleus of a metal is equal to Z.e where ‘e’ is the charge on an electron and ‘Z’ is a constant for the metal known as the atomic number.
2.2 Atomic Models Help the students in solving numericals based on Rydberg’s formula for hydrogen atom with the help of solved numerical through the following guided steps. Problem: If an electron goes from n=3 to n=2 level, what wavelength of light is emitted?
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Unit 11: Structure of Atom
Solution: Step 1: Use the following equation for solving the problem: The Rydberg Equation: "1 1 % = R · $$ 2 ! 2 '' # n1 n1 &
1
R: = 1.0974.107.m–1
!
Step 2: Substitute the values of n1, n2 and R in the above equation to find wavelength.
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"1 1% = (1.0974.107.m–1) · $ 2 ! 2 ' #2 3 &
1
1
1
1
1
1
1
l = 6.5609.10–7.m
l = 656.09 nm
!
!
!
!
!
!
!
"1 1 % = 1.0974.107.m–1 · $$ ! '' # 4 32 & " 1 1% = 1.0974.107.m–1 · $ ! ' #4 9& " 1% = 1.0974.107.m–1 · $.25 ! ' 9& #
= 1.0974.107.m–1 (.25 – .11111) = 1.0974.107.m–1 . (.13889) =
1524178.86 m
Unit 11: Structure of Atom
nm: = 10–9 . m
2.3 Quantum mechanical model Help the students in solving numericals based on de Broglie wavelength and Heisenberg’s Uncertainty principle with the help of solved numerical through the following guided steps. Problem: Calculate the velocity of an electron (mass = 9.10939 × 10¯31 kg) having a de Broglie wavelength of 269.7 pm Solution: Step 1: Convert pm to m: 269.7 pm = 269.7 × 10-12 m = 2.697 × 10-10 m Step 2: Use the de Broglie equation to determine the energy (not momentum) of the atom: l = h/p l = h/√(2Em) 2.697 × 10–10 m = 6.626 × 10–34 J s/√[(2) (x) (9.10939 × 10–31 kg)] Or √[(2) (x) (9.10939 × 10–31)] = 6.626 × 10–34 / 2.697 × 10–10 x = 3.313 x 10–18 J Step 3: Use the kinetic energy equation to get the velocity: KE = (1/2) mv2 3.313 x 10–18 = (1/2) (9.10939 × 10–31) v2 v2 = 7.2738 × 1012 v = 2.697 × 106 m/s Problem: Calculate the de Broglie wavelength of a neutron (mass = 1.67493 × 10–27 kg) moving at one five-hundredth of the speed of light (c/500). Solution: Step 1: Determine the speed of the neutron: 3.00 × 108 m/s divided by 500 = 6.00 × 105 m/s 7
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Unit 11: Structure of Atom
Step 2: Calculate the kinetic energy of the neutron: KE = (1/2)mv2 KE = (1/2) (1.67493 × 10–27 kg) (6.00 × 105 m/s)2 KE = 5.02479 × 10–22 J Step 3: Use the de Broglie equation: l = h/p l = h/√(2Em) l = 6.626 × 10–34 J s/√[(2) (5.02479 × 10
–22
J) (1.67493 × 10–27 kg)]
l = 5.107 × 10–10 m Problem: Calculate the uncertainty in velocity (in m s–1) of an electron (mass 9.11 × 10-31 kg) under the conditions where the uncertainty in position is 4.782 × 10-3 m. Solution: The Heisenberg Uncertainty Principle is given by the inequality involving position and momentum: D × Dp ≥ ħ/2, where ħ is the “Reduced” Planck’s Constant, 1.054 × 10^-32 J s. Remember the definition of the Joule, 1 J = 1 Kg (m^2/s^2), so the inequality becomes: D × Dp ≥ 5.27 × 10^-33 Kg m^2/s. Given ∆x = 4.782x10^-3 m, the inequality becomes Dp ≥ (5.27x10^-33 Kg m^2/s) / (4.782 × 10^-3 m). So, the uncertainty in momentum is Dp ≥ 1.10 × 10^-30 Kg m/s. Since momentum is the product of mass and velocity (p = mv), then dividing by the mass of the electron will give the uncertainty in velocity, Dv ≥ (1.10 × 10^-30 Kg m/s) / (9.11 × 10^-31 Kg). So the answer is Dv ≥ 1.21 m/s. • Help the students in Designation of an orbital by n, l and m quantum numbers. Make them Recognize the various permissible values for each quantum number by performing the following activity. 8
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Unit 11: Structure of Atom
Extension Black body radiation A hot body is observed to emit thermal radiations which are electromagnetic in nature and have higher wavelengths than the visible radiations. The energy of the radiation of a hot body is spread over a continuous spectrum which moves to shorter wavelengths at higher temperature (Fig. (a)). Thus below took the thermal radiations are low energy radiations lying in far infrared region, but shift to red region at red hot and to white region at the incandescent temperature (above 3500 k) 2000 K El RJ P
25 W 1500 K
1000 K 0
0
2
4 l in µm
6
8
Figure 11.1: Spectral distribution of the intensity of radiations from a black body. RJ = Rayleigh-Jean’s equation • W = Wien’s equation • P = Planck’s equation
Absorption A of a body is defined as the fraction of incident light it absorbs. A body which absorbs all the radiations on it, i.e., A = 1 is called a black body. A well insulated cavity with a small hole for the emission of radiations. e.g., a piece of iron with a hole at the centre constitutes a black body. At equilibrium, a black body radiates the same radiations in all the directions.
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Unit 11: Structure of Atom
Extension Photoelectric effect The photoelectric effect is the ejection of electrons from the surface of a metal or from another material when light shines on it [Fig (a)]. The energy of these photoelectrons is proportional to the frequency of the radiation falling upon the metal surface and the number of photoelectrons emitted per second is proportional to the intensity of the incident radiation [Fig. (b)]. Electrons are ejected however only when the frequency of light exceeds a certain threshold value characteristic of the particular metal. For example, although violet light will cause potassium metal to eject electrons no amount of red light (which has a lower frequency has any effect. Einsteen in 1905 applied Planck’s ideas to the photoelectric effect. When a photon with energy hv falls on a metal surface and an electron is ejected with a velocity m, the kinetic energy of the !1 $ escaping electron # mµ 2 & m being the mass of electron must equal "2 % the difference of the energy of the incident photon and energy (wo) necessary to let the electron escape from the surface. Since (w) may also be expressed in terms of the energy of another photon wo = hvo.
Kinetic energy =
1 mu2 2
= hv – hvo = h (v – vo)
If the intensity of light increases only the number of photons reaching the surface increases, which eject greater number of electrons with the same velocity. On the other hand, if the energy of the striking photon is less than hvo, it fails to provide energy for the electrons to escape, and no electrons are ejected regardless the number of photons reaching the surface.
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Unit 11: Structure of Atom
Radiations
Battery
e –
Light
Photoelectric effect
Metal surface
Detector
Current meter
– Vaccum chamber
Battery
Kinetic energy of ejected electrons
Kinetic energy of ejected electrons
Figure 11.2(a): Equipment for studying the photoelectric effect. Light of a particular frequency strikes a clean metal surface inside a vacuum chamber. Electrons are ejected from the metal and are counted by a detector that measures their kinetic energy.
n0 Frequency of Light(n) (a)
Constant
Intensity of Light (b)
Figure 11.2(b): Dependence of kinetic energy of photoelectrons on frequency and intensity of incident radiation.
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Unit 11: Structure of Atom
Student Activity 2 Fill in the following chart: Principal Energy Level (n=?) 1 2
Orbital Types
# of orbitals per level
(sublevels available) s
Total # of orbitals per P.E.L. (n2)
1
Total # of e’s per P.E.L. (2n2)
1
p
3
# of e’s per orbital type
2
6
5
4 14
2.4 Shapes of atomic orbitals Help the students in understanding the concept of shapes of various orbitals by using three-dimensional models available on the internet. The following links may prove useful in doing this. Some Useful links: http://library.thinkquest.org/3659/structures/shapes.html http://www.youtube.com/watch?v=VfBcfYR1VQo http://www.jce.divched.org/jcedlib/livtexts/pchem/jce2005p1880_2ltxt/ quantumstates/bookfolder/l25orbitalshapes.htm http://www.youtube.com/watch?v=F-xLQ1WBIlQ 12
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Unit 11: Structure of Atom
2.5 Rules for filling electrons in orbitals Introduce the following topics and help the students understand these concepts: • Understand and apply Aufbau principle. • Understand the (n+l) rule. • Predict order of energies of orbitals. • State and apply Pauli’s exclusion principle as well as Hund’s rule of maximum multiplicity. • Represent the electronic configuration for any given atom. • Calculate the number of valence electrons for any given element. • Recognize the causes of stability of completely filled and half-filled sub shells. • Understand the concept of exchange pair formation and exchange energy. • Comprehend the contribution of symmetrical distribution of electrons towards stability. The following solved examples may be quoted in order to explain the above concepts: For example: Na+, atomic number = 11, number of positive charges = 1 Number of electrons in Na+ = (11 - 1) = 10 Electronic configuration is 1s2 2s2 2px2 2py2 2p2z . For anions the electronic configuration is written by determining the number of electrons. The number of electrons is found by adding the number of negative charges on the anion to the atomic number. For example: Cl-, atomic number = 17, number of negative charges = 1
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Unit 11: Structure of Atom
Number of electrons in Cl- = (17 + 1) = 18 Electronic configuration is 1s2 2s2 2px2 2py2 2p2z 3s23px2 3py2 3p2z The ions and atoms having the same number of electrons are termed as isoelectronic e.g., O2-, Na+, Al3+, Mg2+ and Ne (each containing ten electrons).
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Unit 11: Structure of Atom
Student Worksheet 1
1. The number of protons in one atom of an element determines the atoms _____________________ , and the number of electrons determines ______________________ of an element.
2. The atomic number tells you the number of ______________________ in one atom of an element. It also tells you the number of _____________________in a neutral atom of that element. The atomic number gives the “identity “of an element as well as its location on the Periodic Table. No two different elements will have the _____________ atomic number.
3. The ______________________of an element is the average mass of an element’s naturally occurring atom, or isotopes, taking into account the ______________________of each isotope.
4. The ______________________of an element is the total number of protons and neutrons in the______________________ of the atom.
5. Give the symbol and number of electrons in a neutral atom of:
Uranium
__________________
Chlorine __________________
Boron
__________________
Iodine
__________________
Antimony __________________
Xenon
__________________
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6. If you know only the following information can you always determine what the element is? (Yes/No).
(a) number of protons ___________
(b) number of neutrons ___________
(c) number of electrons in a neutral atom ___________
(d) number of electrons ___________
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Unit 11: Structure of Atom
Student Worksheet 2 Fill in the chart with the needed information Atomic Number 1
3
Symbol
Atomic Mass
Protons
Neutrons
Electrons
Hydrogen
H
1
1
0
1
Helium
Lithium
Li
Element
7
3
4
2,1
Beryllium
Boron
Carbon
2,4
Nitrogen
Oxygen
Nitrogen
N
14
7
7
2,5
Oxygen
Fluorine
Neon
Sodiuim
Magnesium
Aluminum
Silicon
Phophorous
Sulphur
Ar
40
18
22
2,8,8
Chlorine 18
16
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Argon
Unit 11: Structure of Atom
Student Worksheet 3 A. Multiple choice questions 1. The number of orbitals in a given subshell, such as the 5d subshell, is determined by the number of possible values of (a) n (b) l (c) ml (d) ms
2. What are the possible values of n and ml for an electron in a 5d orbital? (a) n = 1, 2, 3, 4, or 5 and ml = 2 (b) n = 1, 2, 3, 4, or 5 and ml = -2, -1, 0, +1, or +2 (c) n = 5 and ml = 2 (d) n = 5 and ml = -2, -1, 0, +1, or +2
3. How many electrons can a single orbital hold? (a) 2n (b) 2 (c) 2l + 1
4. Which of the following is not a valid set of quantum numbers? (a) n = 2, l = 1, ml = 0, and ms = -1/2 (b) n = 2, l = 1, ml = -1, and ms = -1/2 (c) n = 3, l = 0, ml = 0, and ms = 1/2 (d) n = 3, l = 2, ml = 3, and ms = 1/2
5. What are the possible values of l if n = 5? (a) 5 (b) 0, 1, 2, 3, or 4 (c) -4, -3, -2, -1, 0, +1, +2, +3, or +4 (d) -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, or +5
6. The subshell designations follow the alphabet after f. What is the first shell in which an h orbital would be allowed? (a) fifth (b) sixth (c) seventh (d) eighth
(d) 8
B. Short Answer Type 1. What are quantum numbers?
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2. What information does the first three quantum numbers indicate?
3. What does the fourth quantum number indicate?
4. What does the principal quantum number indicate?
5. The letter, n, is used to designate the principal quantum number (True or False).
6. What does the orbital quantum number indicate?
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Unit 11: Structure of Atom
Student Worksheet 4
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1. Orbital’s with different shapes occupy different regions. These regions are called _____ .
2. The quantum numbers designated in ascending order use the letters _____ .
3. What is the shape of the s orbital?
4. What is the shape of the p orbital?
5. In the nth principal energy level, orbital’s of _____ .
6. What does the magnetic quantum number indicate?
7. There is only one orientation of the s orbital (True or False).
8. How many possible orientations are there for the p orbital? What are these orientations called?
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Unit 11: Structure of Atom
Student Worksheet 5
1. Which sets of quantum numbers are unacceptable? (a) n = 3, l = -2, ml = 0, ms = +½ (b) n = 2, l = 2, ml = -1, ms = -½ (c) n = 6, l = 2, ml = -2, ms = +½ (a) unacceptable, b/c l must be equal to 0, 1, 2, 3 etc (never a negative #) (b) unacceptable, if n = 2 then l can only equal 0 or 1 (not 2 which is d-block) (c) is acceptable
2. Indicate which of the following orbital destinations are possible. (a) 7s (b) 1p (c) 5d (d) 2d (e) 4f (f) 5g (g) 6i b is impossible b/c the 1st energy level or shell only has the s subshell, d is impossible b/c the 2nd energy level only has s & p subshells
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3. Indicate which of the following electron configurations is ruled out by the Pauli exclusion principle. (a) 1s22s22p7 (b) 1s22s22p63s3 (c) 1s22s22p63s23p64s23d12 (d) 1s22s22p63s23p6 4. Explain why the following ground-state electron configurations are not possible: (a) 1s22s32p3 (b) 1s22s22p33s6 (c) 1s22s22p73s23p8 (d) 1s22s22p63s23p14s23d14 5. Apply Hund’s rule as you write the ground-state electron configuration for: (a) O+ (b) C– (c) F+ (d) Ar+ 6. Determine the number of unpaired electrons in the ground-state of the following species: (a) F+ (b) Sn2+ (c) Bi3+ (d) Ar+ 7. Fill in the blanks with the correct response: (a) The number of orbitals with the quantum numbers n = 3, l = 2 and ml = 0 is _________. (b) The number of valence electrons in the outermost p subshell of a sulfur atom is _________.
Unit 11: Structure of Atom
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(c) The number of unpaired electrons in a Mn2+ ion is _________. (d) The subshell with the quantum numbers n = 4, l = 2 is _________. (e) The ml values for a d orbital are ________________________. (f) The allowed values of l for the shell with n = 2 are _________. (g) The allowed values of l for the shell with n = 4 are _________. (h) The number of unpaired electrons in the cobalt atom is _________. (i) The number of orbitals in a shell with n = 3 is _________. (j) The number of orbitals with n = 3 and l = 1 is _________. (k) The maximum number of electrons with quantum numbers with n = 3 and l = 2 is _________. (l) When n = 2, l can be _________. (m) When n = 2, the possible values for ml are _________. (n) The number of electrons with n = 4, l = 1 is _________. (o) The quantum number that characterizes the angular shape of an atomic orbital is _________. (p) The subshell with n = 3 and l = 1 is designated as the ______________ subshell. (q) The lowest value of n for which a d subshell can occur is n = _________. 8. Give two examples of: (a) an atom with a half-filled subshell (b) an atom with a completely filled outer shell (c) an atom with its outer electrons occupying a half-filled subshell and a filled subshell.
Unit 11: Structure of Atom
Crossword Puzzle 1
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5
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7
8
10
11
12
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14 15 16
17 18 19 20
Across
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1. It has a mass of 1.67495 X 10 -24 g.
3. Material used as alpha particle target by 2-Down.
6. There is always some uncertainty about the position and momentum of an electron.
9. Number of outer energy electrons shown in the electron dot diagram of phosphorus.
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Unit 11: Structure of Atom
11. “The smallness of the value of m/e is, I think, due to the largeness of e as well as the smallness of m. There seems to me to be some evidence that the charges carried by the corpuscles in the atom are large compared with those carried by the ions of an electrolyte.” Philosophical Magazine, 44, 293 (1897). 13. Corrosion-resistant transition element with a full d sublevel, and two outer 4s electrons available for reacting. 15. Number of protons in an atom of carbon-14. 16. Number of 3p electrons in an atom of aluminum. 19. It’s the part of a hydrogen atom that contains about 1836/1837 of the mass of the atom. 20. Useful tool for picking up hot crucibles.
Down
1. Atomic number of the most electronegative element.
2. See 3-Across.
4. Wavelength is inversely proportional to momentum.
5. Cathode rays.
7. (12-Down) X 9, (1-Across) X 9, (5-Down) X 10.
8. Student of 2-Down.
10. Deuterium and tritium. 12. Mendeleev didn’t know they existed in 1869. 14. Number of 3d electrons in a ground state titanium atom. 17. Number of 3p electrons in a ground state sulfur atom. 18. Number of electrons in a magnesium ion. 22
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Unit 11: Structure of Atom
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Unit 11: Structure of Atom
Rubrics of Assesment for Learning Parameter Recall the existence of sub atomic particles namely electrons, protons and neutrons in an atom. Know about the Thomson and Rutherford models of atom and list their limitations. Recall the meaning of terms atomic number, mass number, isotopes and isobars. Appreciate the developments which led to Bohr model. Understand the characteristics of Bohr model as well as the causes of its failure. Comprehend the Planck’s quantum theory and Black body radiation phenomenon. Appreciate that radiation and matter show dual behaviour. Solve problems based on De Broglie relation. Understand the concept of quantization of electronic energy levels. Distinguish between orbit and orbital. State the Heisenberg’s uncertainty principle and solve problems based on the same. 24
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Unit 11: Structure of Atom
Beginning Approaching Meeting Exceeding (1) (2) (3) (4)
List the important features of quantum mechanical model. Designate an orbital by n, l and m quantum numbers. Recognize the various permissible values for each quantum number. Understand the origin of electron spin quantum number. Plot the orbital wave functions for s, p and d orbitals. Draw the probability density plots of s, p and d orbitals. Understand the terms: Node and Nodal surface. Calculate the number of nodes for any given orbital. Arrange various orbitals in order of increasing energies and plot their energy level diagrams. Understand the concept of shielding and define effective nuclear charge. Understand and apply Aufbau principle. Understand the (n+l) rule. Predict order of energies of orbitals. State and apply Pauli’s exclusion principle as well as Hund’s rule of maximum multiplicity.
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Unit 11: Structure of Atom
Represent the electronic configuration for any given atom. Calculate the number of valence electrons for any given element. Recognize the causes of stability of completely filled and half-filled sub shells. Understand the concept of exchange pair formation and exchange energy. Comprehend the contribution of symmetrical distribution of electrons towards stability.
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Unit 11: Structure of Atom
Common Misconceptions Although students often think that atoms are solid, they are mostly empty space.
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v
The
use of models often leads to misconceptions. For example, some students think that atoms have a physical bonding agent similar to the toothpicks and skewers used in atomic models. They should understand that models are simple representations of more complex objects.
v
Because
v
Often
v
Often
“the planetary model” is used to represent the orbits of electrons around a nucleus, some people think that electrons travel at a constant rate along a 2-dimensional circle or ellipse, similar to the motion of planets around a sun. Actually, the theory describes a series of different 3-dimensional orbital shapes or clouds in which moving electrons are likely to be found. the Bohr’s orbits are confused with orbitals.
the spectral lines are mistaken to represent energy levels. Spectral lines depict the absorption/emission frequency/energy values and not the energy levels.
Unit 11: Structure of Atom
Additional Resources Links v
www.aip.org/history/electron
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www.experiment-resources.com › Physics Experiments
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isaacmmcphee.suite101.com ›Atomic/Molecular/Optical Physics
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www.timetoast.com/timelines/65274 - United States
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www-outreach.phy.cam.ac.uk/camphy/nucleus/nucleus1_1.htm
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www.rsc.org/chemsoc/timeline/pages/1911.html
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www.einsteinyear.org › facts
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www.iun.edu/~cpanhd/C101webnotes/modern.../Bohr-model.html
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csep10.phys.utk.edu/astr162/lect/light/absorption.html
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http://library.thinkquest.org/3659/structures/shapes.html
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http://www.youtube.com/watch?v=VfBcfYR1VQo
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www.4physics.com/phy_demo/QM_Article/article.html
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www.spaceandmotion.com/quantum-theory-max-planck-quotes.htm
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www.classle.net/faq/what-difference-between-orbit-and-orbital
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www.colorado.edu/physics/2000/elements.../quantum_numbers.html
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ttp://www.jce.divched.org/jcedlib/livtexts/pchem/ h jce2005p1880_2ltxt/quantumstates/bookfolder/l25orbitalshapes.htm
ww.angelo.edu/.../quantum_numbers/Quantum_Numb... - United w States
Unit 11: Structure of Atom
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Unit 11: Structure of Atom
CENTRAL BOARD OF SECONDARY EDUCATION
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