Inorganic chapter 1, Lecture notes of Inorganic Chemistry

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Chapter 1 - Basic Concepts: atoms

Discovery of atomic structure

JJ Thomson (1897)

Milliken (1909)

Rutherford (1910)

Rutherford (1911)

Symbol p+^ e-^ n^0 Mass (amu) 1.00732 0.000549 1. Discovery 1919, Rutherford 1897, Thomson 1932, Chadwick

Atomic and Mass Numbers

C

Symbol

Mass number

Atomic number

(optional)

Atomic number ( Z ): equal to the number of

protons in the nucleus. All atoms of the same

element have the same number of protons.

Mass number ( A ): equal to the sum of the number

of protons and neutrons for an atom.

Atomic mass unit (amu) is 1/12 the mass of 12 C (1.660 × 10-27^ kg)

A

Z

E

Allotropes

element's atoms are bonded together in a different manner

Successes in early quantum theory

= = ^ −

n n

R

where R is the Rydberg constant for H, 1.097×10^5 cm-

λ =

h

mv

where h is Planck’s constant, 6.626×10-34^ Js

(∆ x ) (∆ mv ) ≥

h

4 π

Uncertainty Principle

Wave Nature of Matter

Atomic

Orbital

n l ml Radial part of the

wavefunction, R(r)

Angular part of

the wavefunction, A(θ,φ)

1 s 1 0 0

2 s 2 0 0

2 px 2 1 +

2 pz 2 1 0

2 py 2 1 -

r e

− 2

/ 2 ( 2 ) 2 2

(^1) r r e

− −

/ 2

2 6

(^1) r re

−

/ 2

2 6

(^1) r re

−

/ 2

2 6

(^1) r re

−

2 π

1

2 π

1

π

θ φ

2

3 (sin cos )

π

θ

2

3 (cos )

π

θ φ

2

3 (sin sin )

Atomic Orbitals

A wavefunction ψ is a mathematical function that contains detailed information about the behavior of an electron. An atomic wavefunction consists of a radial component R(r) , and an angular component A(θ,φ). The region of space defined by a wavefunction is called an atomic orbital.

Degenerate orbitals possess the same energy.

1s (^) 2s

Plot of the radial part of the wavefunction against distance ( r ) from the nucleus

( n - l -1) radial nodes

ns orbitals have ( n -1 radial nodes), np orbitals have ( n -2 radial nodes), nd orbitals have ( n -3 radial nodes), nf orbitals have ( n -4 radial nodes).

Plots of radial parts of the wavefunction R ( r ) against r for the 2 p , 3 p , 4 p and 3 d atomic orbitals

Boundary surfaces for angular part of wavefunction, A(θ,φ)

Different colors of lobes are significant

• For s orbital it has constant phase i.e. the amplitude of the wavefunction has a constant sign
• For a p orbital, there is one phase change with respect to the boundary surface. This phase change occurs at a nodal plane.

Representations of an s and a set of three degenerate p atomic orbitals.

Cross-sections through the (a) 1 s (no radial nodes), (b) 2 s (one

radial node), (c) 3 s (two radial nodes), (d) 2 p (no radial nodes)

and (e) 3 p (one radial node) atomic orbitals of hydrogen.

Radial probability functions

Probability density

Spin Quantum Number, ms

•Spin angular number, s, determines the magnitude of the spin angular momentum of a electron and has a value of ½. •Since angular momentum is a vector quantity, it must have direction

•Magnetic spin quantum number, ms, can have values +1/2 or -1/2.

An orbital is fully occupied when it contains two electrons which are spin paired; one electron has a value of ms = +1/2 and the other -1/

ml = 2 +2(h/2 π )

ml = 1 +(h/2 π )

ml = 0 0

ml = -1 -(h/2 π )

6 ( h / 2 π )

6 ( h / 2 π )

6 ( h / 2 π )

6 ( h / 2 π )

6 ( h / 2 π )

ml = -2 -2(h/2 π )

Resultant angular momentum

Resultant magnetic moment

Angular momentum, the inner quantum number, j, spin-orbit coupling

z component of orbital angular momentum

orbital angular momentum

(^1) H – ground state Many-electron atom

Ground State Electronic Configurations

The sequence that approximately describes the relative energies or orbitals in neutral atoms: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p< 5s < 4d < 5p < 6s <5d≈4f < 6p < 7s < 6d≈5f

Effective nuclear charge

Z eff = Z – S

Slater's Rules for Calculating Shielding

1. Write out electron configuration of the element

[1s][2s,2p][3s,3p][3d][4s,4p][4d][4f] [5s,5p] etc*

2. Electrons in an group higher in this sequence contribute

nothing to S.

3. For an electron in ns or np orbital

i. Each of the other electrons of same group contributes S =

0.35 each (except in 1s, S = 0.3)

ii. Each electron in (n – 1) shell , contributes S = 0.

iii. Each electron in (n – 2) or lower shell , contributes S = 1.

4. For an electron in an nd or nf group

i. Each of the other electrons of same nd or nf group contributes

S = 0.35 each

ii. Each electron in a lower group , contributes S = 1.

*A bracket indicates a group and n is the principle quantum number of a shell

The aufbau principle

•Orbitals are filled in the order of energy, the lowest

energy orbitals being filled first.

•Hund’s first rule: in a set of degenerate orbitals,

electrons may not be spin paired in an orbital until

each orbital in the set contains one electron; electrons

singly occupying orbitals in a degenerate set have

parallel spins, i.e. have the same values of ms.

•Pauli Exclusion Principle : no two electrons in the

same atom can have identical sets of quantum

numbers n, l, ml, ms; each orbital can accommodate a

maximum of two electrons with different ms.

Ionization Energy

Electron Affinity

Electron affinity is

defined as minus the

change in internal

energy for the gain of

an electron by a

gaseous atom.

EA = -ΔU(0K)