l16 chapt9-3 web

Chemistry 5 Chapter-9 Electrons in Atoms Part-3 1/2 done

30 October 2002

1/2 done

p-orbitals (l = 1) ƒ Key features: • 1- angular node at r = 0. • probability density is not spherically symmetric; 2-lobed orbitals

• Three degenerate p-orbitals: ml = 0, ±1 • n-2 radial nodes in wave function signs (+, -) correspond to phases of wavefunction, ψ, and do not signify charge. n = 2; l = 1

n = 3; l = 1

d-orbitals (l = 2)

ƒ Key features: • Two angular nodes at r = 0. • probability density is not spherically

symmetric; four-lobed orbitals designated with respect to x,y,z axes

• Five degenerate d-orbitals; ml = 0, ±1, ±2 • n-3 radial nodes in wave function

signs (+, -) correspond to phases of wavefunction, ψ

Orbitals– Summary ƒ Variation of n for fixed l For a given value of l, and increase in n leads to an increase in the average distance of electron from nucleus and thus average size of orbital.

ƒ Nodal properties An orbital with quantum numbers n and l has l angular nodes and n – l – 1 radial nodes with total of n – 1 nodes. For 1-electron atom energy depends only on the total number of nodes (i.e., n, but not l or m).

ƒ Probability at nucleus As r approaches zero, ψ vanishes for all orbitals except s. Hence, electrons in s orbitals are said to penetrate to the nucleus.

Electron Spin ƒ Experimental observation? A beam of atoms, which have an odd number of electrons, is split into two component when passed through an inhomogeneous magnetic field: Stern Gerlach experiment.

ƒ Electron Spin Quantum Number, ms This observation can be explained by introducing a fourth quantum number, the spin quantum number, ms = ±½ , where “+” signifies spin up (↑), and “-” spin down (↓). Qualitatively, this can be thought of in classical picture where spinning electron creates magnetic field (but don’t take too literally!).

Multielectron Atoms ƒ Moving beyond hydrogen atom?

ƒ Subshells within a shell lose their degeneracy due to the interactions between electrons.

Electron Configurations Given a set of orbitals, how are these filled with electrons? ƒ Minimize energy:

Electrons occupy (are added to) orbitals in way that minimizes the energy of an atom; this generally means starting with subshells of sequentially higher principle quantum number. The general order is: 1s; 2s, 2p; 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s,…

ƒ Pauli exclusion principle:

No two electrons in an atom may have the same 4 quantum numbers Î if two electrons occupy the same orbital then these electrons must have opposite spins, ms = ±½ . Hence, the electron capacity of a given subshell is 2x orbital degeneracy: s subshell can hold 2 electrons; p subshell can hold 6 electrons.

ƒ Hund’s rule: When orbitals of the same energy are available– degnerate orbitals– electrons occupy orbitals singly with spin parallel; alternatively, maximize the number of unpaired electrons in degenerate orbitals.

Lets apply these ideas – look at real atoms!

Building Up Atoms: Start Simple 1s ƒ Hydrogen: 1 electron

2p

↑

1s ƒ Helium: 2 electrons

2s

1s1

2s

2p 1s2

↑↓

1s

2s

↑

↑

2p 1s12s1 excited state

• orbital diagram– breaks each subshell into individual orbital boxes, which are filled with electrons of spin up/down configuration. • spdf notation– shows number of electrons in each subshell starting with lowest principle quantum number

Building Up Atoms: More Interesting Examples? 1s

2s

↑↓ 1s

↑ 2s

↑↓

↑↓

1s

2s

↑↓

↑↓

1s

2s

↑↓

↑↓

1s

2s

ƒ N

↑↓ 1s

↑↓ 2s

↑

ƒ O

↑↓

↑↓

↑↓

1s

2s

ƒ F

↑↓ 1s

ƒ Ne

↑↓

ƒ Li ƒ Be ƒ B ƒ C

2p

1s22s1 or [He]2s1 2p

1s22s2 or [He]2s2 2p

1s22s22p1 or [He]2s22p1

↑ 2p ↑

↑

1s22s22p2 or [He]2s22p2

2p ↑ ↑ 2p

1s22s22p3 or [He]2s22p3

↑

↑

1s22s22p4 or [He]2s22p4

↑↓ 2s

↑↓ ↑ ↓ ↑ 2p

1s22s22p5 or [He]2s22p5

↑↓

↑↓ ↑↓ ↑↓

1s22s22p6 or [He]2s22p6

2p

Periodic Trends: Beginning H 1s1

He 1s2

Li 2s1

Be 2s2

B 2p1

C 2p2

N 2p3

O 2p4

F 2p5

Ne 2p6

Na 3s1

Mg 3s2

Al 3p1

Si 3p2

P 3p3

S 3p4

Cl 3p5

Ar 3p6

K Ca Sc

Examples: 1. Phosphorous, P:

[Ne]3s23p3

2. Calcium, Ca:

[Ar]4s2

3. Scandium, Sc:

[Ar]3d14s2

Periodic Trends: Overview & Predictions

Examples: 1. Thallium, Tl: [Xe]4f145d106s26p1 2. Neodymium, Nd: [Xe]4f35d16s2