H2 Quantum Physics_Part 1 Tutorial 2014_Student

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JC1 Physics 2006 JC2 H2 PHYSICS 2014 Chapter 18: Quantum Physics [Part 1]

Section A: Review of Concepts This section helps you to consolidate your learning for this chapter. Complete the following summary of concepts before attempting the tutorial questions; all answers can be found in your lecture notes. I)

Photoelectric Effect

(a) i. In the space provided below, draw a well-labelled sketch for the set-up of the Photoelectric experiment.

ii. Briefly describe how the experiment is conducted to show photoelectric effect. • ……………… E and ……………… C are contained in an ………………….. glass tube with

a

………………

window

that

permits

the

passage

of

………………

and …………………………... • The …………………………………………………. maintains electrodes at ………………. known potentials. The …………………….. allows the measurement of current between electrodes. (b)

Describe the observations of the photoelectric experiment.

1. Existence of …………………………………… For a given metal, ………………………………………………………………………………… ……………………………………………………….., no matter what the intensity of the incident radiation is or for how long it falls on the surface.

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2. Emission is ………………………. ………………………………………………………………………………………………………… ………………………………, with no detectable time delay. It does not dependent on the intensity of the incident radiation. 3. Max K.E. is .................................................................................. Photoelectrons emitted from a metal have a range of velocities from zero up to a maximum vmax. ………………………………………………………………………………………………………… …………………………………………………………………………………………………………. 4. Rate of ………………………………………………….. For a given frequency, ………………………………………………………………………........... (c)

Explain what is meant by photon? Give the formula for the energy E of a photon of frequency f. …………………………………………………………………………………………………………… hc E = hf =

λ

(d)

Explain what is meant by photo-electrons?

…………………………………………………………………………………………………………… …………………………………………………………………………………………………………… (e)

State the photoelectric equation:

Energy Input (by photon) = hf

(f)

=

Minimum work needed to remove a free electron

Φ

+

Excess Ek

+

Ek max

Explain what is meant by the following terms:

1. work function of a metal ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… 2. threshold frequency ………………………………………………………………………………………………………… …………………………………………………………………………………………………………

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(g) Explain why the maximum photoelectric energy is independent of intensity whereas the photoelectric current is proportional to intensity. An

electron

is

emitted

if

it

gains

enough

energy

from

the

photon.

Since ……………………………….. is delivered …………………….. to the electron in a ………………………………, there is …………………………………. and is independent on the intensity of the incident radiation. Since intensity of a beam of photons is the …………………………………………………………

I = …………, where n is the number of photons passing a unit area per unit time. An increase in intensity means a ……………………………………………………………………… and therefore greater number of electrons can be emitted. (h) Graphical Representation

Observations

Stopping potential VS plotted against frequency f for three different metals.

• The respective threshold frequencies are different because the metals have …………………………………………. • But, the slope of the three lines is the …………… since the slope is given by ………... (Recall that VS =……………….……….)

Fig. i A metal is illuminated by monochromatic light of a given wavelength λ which is below the threshold wavelength for the metal.

• When the ………………………………….. V is increased negatively, the stopping potential VS is the …………. for a beam of …………..…………. P and one of ………………………. Q. • When V is …………….. all the photoelectrons are collected so that the …………………. is ……………….. • A beam of high intensity Q produces …………………………. than one of low intensity P. If Q is twice the intensity of P,

Fig. iii

the current I is …………… as much.

Variation of current with intensity

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for a given wavelength λ below the threshold value

• The photocurrent I (rate of emission of photoelectrons is …………………….. to the intensity of light (rate of photons incident) and a ……………………………... graph is obtained

Fig. ii

II) Wave Particle Duality h p

(a)

The de Broglie wavelength of a particle is given by λ =

(b)

State how the wave nature of electromagnetic radiation is demonstrated.

……………………………………………………………………………………………………… (c)

State how the particulate nature of electromagnetic radiation is demonstrated.

………………………………………………………………………………………………………… (d)

State how the wave nature of a particle is demonstrated.

………………………………………………………………………………………………………… (e)

State how the particulate nature of a particle is demonstrated.

………………………………………………………………………………………………………… III) Energy Diagrams and Line Spectra (a) Describe the behaviour of an electron using an energy-level diagram. An energy-level diagram is a useful pictorial representation of the stationary state energies. Each stationary state corresponds to a different amount of …………………... Electrons are found

in

these

stationary

states.

Electrons

inside

atoms

have ………………………………………. of energy. The …………………………………. refers to the lowest energy level (n = 1 for Hydrogen) in which the atom is the ………………………….

The electron normally occupies this level

unless given sufficient energy to move up to a higher level.

An atom is said to be in

an ……………………………… when its electrons are found in the higher energy levels.

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When an atom is excited from the ground state to a higher energy level, it becomes

………………

and

falls

back

to

one

of

the

lower

energy

levels

by …………………………………………………………………………………………….. (b) The presence of energy levels in atoms are demonstrated by emission spectra and absorption spectra. 1. Explain how an emission spectrum looks like and how it is formed. Emission line spectrum consists of …………………………………………………………..


………... such as hydrogen or neon can be placed in a ………………………………… A ……………….. is applied between metal electrodes in the tube which is large enough to produce an ………………………….. in the gas.




The gas becomes ……………….....................................................……………………, from cathode to anode of the discharge tube.




The excited gas atoms are ………………. When the gas atoms fall to a lower energy level, ……………………….……………............................................................…………..




The

frequency

f

of

the

emission

line

is

dependent

……………………………………………………………………………….,

∆E

on =

the hf.

Because only certain high  low energy level transitions are possible within the atom, therefore only ………………………………………………………………………..


No two gases give the same exact line spectrum.

2. Explain how an absorption spectrum looks like and how it is formed. An absorption spectrum consists of ………………………………………………………………..


It is produced when ………………………………………………………………………….. When white light passes through a cooler gas, the atoms of the cooler gas absorb …………......................................................................................................…..




The excited atom does not retain the energy but ……………….…………………………




………………………………………..

Consequently,

the

parts

of

the

spectrum

corresponding to these wavelengths appear ……………….. (or “missing”) by comparison with the other wavelengths not absorbed. (c)

The emission or absorption line spectrum is due to the many possible transitions between any two energy levels of an atom. The energy of the photon emitted or absorbed is the difference between the two energy levels: given by ∆E = Ef − Ei = hf =

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λ

5

Section B: Question-Solving Photoelectric Effect 1.

Which one of the following is a correct statement of an observation of the photo-electric effect? A

Photo-electric emission takes place instantaneously because a single photon transfers all its energy in a concentrated packet to the surface electron.

B

Regardless of the incident frequency, no photo-emission will take place unless the intensity is above a certain threshold value.

C

For any given radiation wavelength, the higher the work-function of the metal, the higher will be the maximum kinetic energy of the emitted photo-electrons.

D

The stopping potential for any given experiment depends only on the type of metal used, and is independent of the wavelength of the incident radiation.

Students’ Thinking Box : • Recall the observations from the Photoelectric Experiment?

2.

In a photoelectric emission experiment using light of a certain frequency, the maximum kinetic energy Ek of the emitted photoelectrons is measured. Which graph represents the way in which Ek depends on the intensity I of the light? A

B Ek

Ek

I

0

C

D

Ek

0

3.

I

0

Ek

I

0

I

Using this Photoelectric Effect applet from this link: http://phet.colorado.edu/simulations/sims.php?sim=Photoelectric_Effect For these metals, Sodium, Platinum and Calcium, determine for each metal, (a) their work function in eV, (b)

their stopping potential when a wavelength of 170 nm is incident on them and

(c)

hence, the maximum kinetic energy of the outgoing photoelectrons.

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4.

In a photoelectric emission experiment, a metal surface in an evacuated tube was illuminated with light. Fig. 4.1 below shows the stopping potential Vs as a function of the frequency f of the incident light falling on the metal surface.

Fig. 4.1

(a) Explain what is meant by (i) work function of a metal and (ii) the stopping potential. (b) (i)

Deduce the value of Planck’s constant from Fig. 4.1.

(ii) Determine the work function for this metal, expressing it in electron-volts. (iii) If the electrons emitted from the metal constitute a current of 0.10 µA, calculate the rate at which photoelectrons are ejected. (iv) The stopping potential is 4.0 V when a new incident light frequency is used. Only one in three of the incident photons at this frequency succeeds in ejecting a photoelectron. Calculate the light power incident on the cathode. (v) Explain the observation that the graph in Fig. 4.1 does not extend below the horizontal axis (vi) If a different metal were used, state one feature of the graph which you would expect to remain the same and one feature which you would expect to be different. (vii) Suggest why the tube for the photoelectric experiment needs to be evacuated. (viii)The work function of a certain metal in air increases over time. Suggest a reason why. [6.6 x 10-34 J s, 5.4 eV, 6.25 x 1011 s-1, 2.8 µW]

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5. (a) A source of ultraviolet light has wavelength 2.55 x 10-7 m. Calculate the energy of a photon of this wavelength. (b) The source referred to in (a) illuminates a zinc plate which has been cleaned and placed a few millimeters beneath a piece of gauze as shown below in Fig 5a. Photoelectrons are emitted from the plate and attracted to the positive gauze due to the potential difference V between the plate and the gauze. When V is varied it is found that the photoelectric current varies as shown in curve A in Fig 5b.

Fig 5a (i)

Fig 5b

Explain why, for curve A, the photoelectric current reaches a maximum value no matter how large V is made.

(ii) The battery connections are reversed so that the potential difference V is made negative. Photoelectrons are now replled, but some still reach the gauze. Explain why this is so. (c) (i)

The intensity of illumination is then increased and the experiment repeated to obtain curve B. Explain why the photoelectric current is increased.

(ii) Suggest why the value of V necessary to prevent any photoelectric current remains constant. Students’ Thinking Box : • How do the observations relate to photon energy, number of photons, frequency and intensity. • Since the question focus on the graphical representation of the photoelectric effect, you may want to recall some of the graphical representations of the photoelectric effect. 6. (a) A 20 W point source of light emits monochromatic light of wavelength 530 nm. Determine is the intensity of the light at a distance 5.0 m from the source. (b) In 1 m2 of area at this distance, determine the number of photons detected per second. (c) A 3.0 cm2 metal is place 5.0 m from this point source. Calculate the threshold frequency if the work function energy of this metal is 2.8 x 10-19 J. (d) Hence use the concept of conservation of energy to explain why photoelectric is possible. Show any necessary calculation. (e) Calculate the stopping potential for this photoelectric effect experiment. (f)

If the probability of ejecting the electron is 0.05, calculate the electron current. [0.0637 Wm-2, 1.70 x 1017, 4.22 x 1014 Hz, 0.596 V, 4.08 x 10-7 A]

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Wave-Particle Duality 7.

A parallel beam of violet light of wavelength 4.5 x 10-7 m and intensity of 700 W m-2 is incident normally on a surface. (a) Calculate the energy of a photon of violet light. (b)

Calculate the number of photons incident on 1.0 x 10-4 m -2.

(c)

Calculate the change in momentum of the photons incident on 1.0 x 10-4 m -2 of the surface in 1 second. Assume that the photons are absorbed by the surface.

(d)

Suggest why the quantity you have calculated in (c) is referred to as ‘radiation pressure’. [4.42×10-19 J, 1.58×1017 s-1, 2.32×10-10 Ns] Students’ Thinking Box : • Recall the definition of intensity. • Recall and use the relation for the de Broglie wavelength and how it relates to change in momentum. • How is pressure related to the part we calculated earlier on change in momentum?

8.

An electron is accelerated through a potential difference of 6.0 kV from rest. Calculate the de Broglie wavelength of this electron. A

1.2 × 10−7 m

B

1.6 × 10−11 m

C

2.3 × 10−15 m

D

1.4 × 10−41 m

Students’ Thinking Box : • Question states that the electron is accelerated hence there must be a change in its kinetic energy. • The electron would gain KE at the expense of _______________________. • How is the expression for KE related to the expression for de Broile wavelength? You may need to manipulate the expressions to see the relation.

9.

A hydrogen lamp is found to produce blue light. The wavelength of the light is 4.9 x 10-7 m. A metal surface has a work function energy of 1.80 eV. Determine the de Broglie wavelength of a photoelectron emitted by a photon of the blue light incident on the metal surface.

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Energy Diagrams & Line Spectra 10.

An energy level diagram for an atom is shown drawn to scale. The electron transitions give rise to the emission of a spectrum of lines of wavelength λ1, λ2, λ3, λ4, λ5.

λ4

λ1

λ2

λ5

λ3

What can be deduced from this diagram? A λ1 > λ2 B

λ3 = λ4 + λ5

C

λ4 has the shortest wavelength.

D

The transition corresponding to wavelength λ3 represents the inonisation of the atom.

Students’ Thinking Box : • How does line spectra relate to the changes in energy in an atom? • Recall that when an electron de-excites from a higher energy level to a lower energy level, a photon will be emitted. How to determine the energy of the photon emitted? • Relate energy of photon to the wavelength of the photon emitted.

11.

The diagram shows part of a typical line emission spectrum. This spectrum extends through the visible region of the electromagnetic spectrum into the ultraviolet region.

X Which statement is true for emission line X of the spectrum? A It has the longest wavelength and is in the ultraviolet end of the spectrum. B

It has the highest frequency and is at the ultraviolet end of the spectrum.

C

It has the lowest frequency and is at the red end of the spectrum.

D

It has the shortest wavelength and is at the red end of the spectrum.

Students’ Thinking Box : • What does each line represent in this line emission spectrum? • What does the gap or spacing between the lines represent?

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12. (a)

A hydrogen lamp is found to produce red light and blue light. The wavelengths of the light are 6.6 x 10 -7 m and 4.9 x 10-7 m. Explain why light of specific wavelengths are produced in the lamp.

(b) The diagram below illustrates some of the electron energy levels in an isolated atom of lithium. 0 -0.67 eV -0.94 eV -1.43 eV

-2.99 eV

-5.73 eV A

B

C

D

-8.68 eV

(i)

The outer electron of a lithium atom is found in the lowest energy level shown. How many joules of energy are required to remove this electron from the atom?

(ii) Which transition A, B, C, D would lead to emission of radiation of the shortest wavelength? (iii) Calculate the wavelength of this radiation. (iv) State the region of the electromagnetic spectrum in which this radiation lies. (v) Sketch the appearance of the spectrum which these four transitions produce. (vi) On the figure above, draw four transitions of greater energy change which give rise to another set of wavelengths. (vii) The work function energy of lithium differs from the energy required to remove the outer electron from an isolated lithium atom. Suggest why this is so. [1.39 x 10-19 J, 2.45 x 10-7 m]

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13. (a)

Fig. 13.1 shows a cooler region of hydrogen gas surrounding a hot gas cloud emitting white light. cool hydrogen gas

Q hot gas cloud (white light source)

P Fig. 13.1

(i)

State and explain the type of hydrogen spectrum observed from point P,

(ii) point Q. (b) Some of the energy levels of an atom X are shown in Fig. 13.2 below.

Energy / 10-17 J 0.00

F

-2.13 -2.19 -2.30 -2.43

E D C B

-4.11

A (ground state)

Fig. 13.2 (i)

Cool vapour of X at low pressure is bombarded with electrons of kinetic energy 1.86 x 10-17 J. State the transitions you would expect to observe.

(ii) If the electrons were replaced with photons all of the same energy, comment on the difference in your observation.

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Section C: Assignment

14. (a) (b)

Deadline: ___________________

Explain what is meant by the photoelectric effect.

[2]

Fig. 14.1 shows the experimental setup used to investigate the photo-electric effect.

Fig. 14.1 The frequency f of the incident radiation is first increased to obtain the graph shown in Fig. 14.2 where I is the current obtained in the ammeter. The frequency is then kept constant but the voltage V is varied to obtain the graph shown in Fig. 14.3. The intensity of the radiation was kept constant throughout the experiments.

Fig. 14.2

Fig. 14.3

Deduce from the graphs the following: (i) The number of photo-electrons emitted in 1 minute.

[2]

(ii) The work function of the metal.

[1]

(iii) The wavelength of the incident radiation.

[2]

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(iv) In Fig. 14.4, draw a graph of photocurrent vs voltage for a third experiment where the intensity of the incident radiation is increased and a metal with a greater work function is used. Label this line ‘B’. [2]

Fig. 14.4 Energy/ eV (c)

-0.54

5 4

486.1 nm

3 656.3 nm

P

-1.51

434.0 nm

2

-3.40

1

-13.60 Fig. 14.5

Fig. 14.5 represents a typical energy-level diagram (not to scale) for hydrogen atoms. (i)

Describe what would happen when an atom makes a transition from one energy level to a lower level. [1]

(ii) Explain why each of the transitions gives rise to a spectrum line.

[2]

(iii) Determine the wavelength of the spectrum line which corresponds to transition P. [3] (iv) An electron of energy 20.0 eV collides with a hydrogen atom in its ground state. The atom is excited to level 2 and the electron is scattered with reduced velocity. The atom subsequently returns to its ground state with emission of radiation. Determine the velocity of the scattered electron. [3] (d)

Electromagnetic waves have a wave nature as well as a particulate nature. This is known as wave/ particle duality. Describe a situation in which particles can be shown to have a wave nature. [2]

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Section D: Additional Questions 15. (a)

Transitions between three energy levels in a particular atom give rise to three spectral lines of wavelengths, in order of increasing magnitude, λ1, λ2, λ3. Give the equation which correctly relates λ1, λ2 and λ3 (i.e. give an equation that links the three wavelengths).

(b) The diagram below shows some energy levels for the hydrogen atom. -0.54 eV -0.85 eV

n=5 n=4

-1.51 eV

n=3

-3.40 eV

n=2

-13.60 eV

n=1

A line spectrum is produced when electrons make transitions down to the n = 1 state. Show quantitatively that this spectrum cannot lie within the visible region of the electromagnetic spectrum. 16.

A photoemissive cell in which the emitter and the collector are of the same metal is connected as shown in Fig.16.1.

A collector

+ V

variable d.c. supply

− emitter

Fig. 16.1

The emitter of area 0.45 cm2 is illuminated with monochromatic radiation of wavelength 300 nm and intensity 180 W m−2. The current I in the circuit is measured for various values of the applied potential difference V between the collector and emitter. The variation of I with V is shown in Fig. 16.2.

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I / nA

4.0

V/V −0.9

0

1.5 Fig. 16.2

(a)

If the intensity of light is now doubled, how will the current and the maximum velocity of the electrons be affected by the intensity of light?

(b) 1.

From the graph in Fig. 16.2, explain why the current remains at a constant value of 4.0 nA when V is equal or greater than 1.5 V,

2. I is not zero even when V is zero. (c) 1. Calculate the rate of incidence of photons on the emitter. 2. Calculate the rate of emission of electrons when V = 1.5 V. (d)

By comparing the values from (c), suggest a reason why the rate of emission of electrons is different from the rate of incidence of photons on the emitter. [1.2 × 1016 s-1, 2.5 × 1010 s-1]

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17. (a)

A fluorescent tube is filled with mercury vapour at low pressure. In order to emit light, the mercury atoms must first be excited. Explain what is meant by an excited mercury atom.

(b) Fig. 17.1 below shows some of the energy levels of the mercury atom. Level 1 represents the lowest possible energy level. (The diagram is not drawn to scale.) Energy / eV

Level n

0 -0.70

∞ 6

-1.54

5

-2.69

4

-3.71

3

-5.72

2

-10.38

1 Fig. 17.1

(i) Explain how Fig. 17.1 can be used to account for the emission spectrum. (ii) In a discharge tube, cool mercury vapour is bombarded with a stream of electrons that have been accelerated from rest through a potential difference of 7.3 V. 1. State and explain how many different frequencies of electromagnetic radiation will be emitted by the mercury vapour. 2. Calculate the longest wavelength of the electromagnetic radiation emitted. (iii) State the amount of energy, in electronvolts, required to ionise a mercury atom. [3, 618x10-9 m, 10.38 eV]

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