Electronic configuration of Atom

Lecture 7

Week 4

Wave Mechanics

• In 1924, de Broglie proposed that if energy is particle like, perhaps matter is wavelike

• According to his theory, e-, p+ and even atom, when in motion possessed wave properties and could be associated with λ, ν and А = this is WAVE MECHANICS

• For light: E = h = hc / • For particles: E = mc2 (Einstein)

L. de BroglieL. de Broglie(1892-1987)(1892-1987)

for particles is called the de Broglie wavelength

Therefore, mc = h /

and for particles (mass)x(velocity) = h /

From previous lecture we know that, Light as well

as heat energy exhibits both wave and particle nature

under suitable conditions = Wave

mechanical theory

• If particle travel in waves, e should exhibit diffraction & interference

- in 1927, Davisson & Germer guided a beam of electrons at nickel crystal and obtain a diffraction pattern. Ex: see Fig. 7.14 of page 271 of your reference Silberg Chemistry book

• Do a math:

a) a stone of mass 100gm moving with a velocity 10m/s. What is the de Broglie’s λ for the stone?

b) an e in H atom has a mass 9.1091×10-28 gm and

moves with a velocity 2.188×10-8 cm/s. what is

the de Broglie’s λ?

Wave length of X-rays is 1nm = 1×10-9 m.

Compare X-rays λ with de Broglie’s λ.

Uncertainty PrincipleUncertainty Principle

• If an e has the properties of both a particle and a wave, so we should be able to determine the location of e in the atom.

• In 1927, W. Heisenberg postulated, The Uncertainty principle, which states that it is impossible to know simultaneously the exact position and momentum (velocity) of a particle/ electron. Heisenberg’s relationship is:

Δx. m Δ u ≥ h/2π This uncertainty product is negligible

in case of large objects

• It means that we can not assign fixed path for e, such as circular orbits of Bohr’s model

• At best we can do is find the probability of finding an e with a probable velocity.

W. Heisenberg1901-1976

So, in macroscopic

world, a moving particle has a

definite location at any instant and a wave is spread out in

space.

• Using this idea, Schrodinger developed a mathematical model based on wave mathematics to describe the position of e in an atom=calculation of the probability of finding e at various points at atom.

• For a given atom, Schrodinger's Equation has many solutions, and each solution is associated with a given wave functions, Ψ, a mathematical description of electron’s motion, also called Atomic Orbital.

E. SchrodingerE. Schrodinger1887-19611887-1961

0.).(8

2

2

2

2

2

2

2

2

EPE

h

m

dz

d

dy

d

dx

d

Ψ does NOT does NOT describe the describe the

exact location exact location of the electron, of the electron,

but but Ψ 22 is is proportional to proportional to the probability the probability of finding an e- of finding an e- at a given pointat a given point

ORBITAL

22 is proportional to the probability of finding an e- at a given point. is proportional to the probability of finding an e- at a given point.

The three dimensional region within which there is higher probability that an e having certain energy will be found is called ORBITAL,The energy of e in an orbital is always same

• By examining the probabilities given by a particular orbital, a "shape" of the orbital can be seen. This shape represents a space around the nucleus that the electron is most likely to be found.

• The many solutions to Schrodinger's equation can be classified by the shape that is from their probability distributions, called orbital, like s, p, and d-type, as shown above. Most orbital types have several possible orientations too.

• An atomic orbital is specified by three quantum numbers.

• One is related to orbital’s size, another its shape third its orientation in space

Quantum number of an atomic Orbital

Those are principal (n), angular (l), and magnetic (m) quantum numbers

n l m

principal

1, 2, 3, …

size and energy

angular momentum

0, 1, 2, …, (n - 1)

shape

magnetic

-l, …, l

orientation

Quantum number of an atomic Orbital

• Those are the principal (n), angular momentum(l), and magnetic (m) quantum numbers.

• The principle quantum number (n):

It actually denotes the principal shell/energy level to which electrons belongs at the atom. It represents the avg. size of atom. Incase of H atom it represents the only orbital of it.

n is a positive integer (1,2,3,…….7)

• In n’th energy level, atom can have only 2n2 number of electrons

Principal quantum number (n) 1 2 3 4

Max. number of electrons in n’th shell/level 2 8 18 32

n = 1 l = 0 = (1s)

n = 2 l = 0, 1 = (2s, 2p)

n = 3 l = 0, 1, 2 = (3s, 3p, 3d)

n = 4 l = 0, 1, 2, 3 = (4s, 4p, 4d, 4f)

designated by letters

l = 0 s orbital

l = 1 p orbital

l = 2 d orbital

l = 3 f orbital

Angular momentum quantum number (l)It is an integer from 0 to (n-1)It is related to the shape of the orbital

n = 1 l = 0 m = 0

n = 2 l = 0 m = 0

l = 1 m = -1

m = 0

m = 1

n = 3 l = 0 m = 0

l = 2

l = 1 m = -1

m = 0

m = 1

m = -2

m = -1

m = 0

m = 1

m = 2

s

s

p

s

p

d

1

1

3

3

1

5

Magnetic quantum number (l)It is an integer from –l through 0 to +lIt is prescribes the orientation of the orbital in space around nucleus

For, n = 1, l = 0 and m = 0

There is only one subshell and that subshell has a single orbital

(m has a single value ---> 1 orbital)

This subshell is labeled s and we call this

orbital 1sEach shell has 1 orbital

labeled s. It is SPHERICAL in

shape.

An atomic orbital is An atomic orbital is defined by 3 quantum defined by 3 quantum numbers:numbers: nn ll m

Electrons are arranged in Electrons are arranged in

shellsshells and and

subshells subshells of of

ORBITALSORBITALS ..nn shell shell

ll subshell subshell

mm designates an designates an

orbital within a orbital within a subshellsubshell

Shells and Subshells

p Orbital & d Orbital

For n = 3,

what are the values of l?

l = 0, 1, 2

and so there are 3 subshells

in the shell.

• For l = 0, ml = 0

s subshell with single orbital

• For l = 1, ml = -1, 0, +1

p subshell with 3 orbitals

• For l = 2,

• ml = -2, -1, 0, +1, +2

d subshell with 5 orbitals

For, n = 2, l = 0 and 1For, n = 2, l = 0 and 1

There are 2 types of There are 2 types of orbitals orbitals

— — 2 subshells2 subshells

For l = 0For l = 0 mmll = 0 = 0

this is a s subshellthis is a s subshell

For l = 1 mFor l = 1 mll = -1, 0, = -1, 0,

+1+1

this is a p subshell this is a p subshell with 3 with 3

orbitalsorbitals

1s orbital

spherical

Shape of Atomic Orbital

See Fig-7.17 of Silberg Chemistry Page 278

Shape of 2p Orbital

dumbbell shape

3p, 4p, 5p etc. are similar shapes but larger size

n = 3, l = 1 Orbitals (3px 3py 3pz )

3d orbitals

cloverleaf

larger nsame shapes but size larger

Representation of 4f Orbitals

Also see Fig - 7.17 & Fig - 7.18 & Fig – 7.19 and Fig - 8.9of your reference Silberg Chemistry Book

2

1

3dn=

3

There are

n2

orbitals in the nth SHELL

Spin Quantum Number (s)

• The spin quantum value indicates that the electron is spinning on its axis in one direction (clockwise/anti clockwise) or the opposite.

• It can have a value of -1/2 or +1/2 only

• The value of s does not depend on any other quantum number

• These spins are also designated by arrows pointing upwards and downwards as

Do this math

• Which of the following sets of quantum numbers are not allowable and why?

a) n= 2, l=2, m=0, s=+1/2

b) n=2, l=0, m=-2, s=-1/2

c) n=3, l=2, m=+2, s=-1/2

• What designation are given to the following orbital?

a) n=4, l=3

b) n=5, l=0

c) n=2, l=1

• Write the missing quantum numbers & sublevel names

n l m name

a) ? ? 0 4p

b) 2 1 0 ?

c) 3 2 -2 ?

d) ? ? ? 2s

Pauli’s exclusion principle

• In 1925, Wolfgang Pauli discover the principle that governs the arrangements of electrons in many electron atoms

• The Pauli exclusion principle states that no two electrons in an atom can have the same set of four quantum numbers n, l, m, s.

• For a given orbital, thus e value of n, l,m are fixed

• Thus if we want to put more than one e in an orbital and satisfy the Pauli exclusion principle, our only option is to assign different values of s to those two e

• We know that their can be only two ss value possible for e

• We conclude that, an orbital can hold a max. of two e, and they must have opposite spin.

Example of Pauli’s Exclusion Principal:

• Consider the second shell (n=2)

• There are 4 orbitals, one s orbital (l=0) and three p orbitals (l=1)

n l m s

2 0 0 +1/2

2 0 0 -1/2

2 1 +1 +1/2

2 1 +1 -1/2

2 1 -1 +1/2

2 1 -1 -1/2

2 1 0 +1/2

2 1 0 -1/2

2 e are in 2s orbital

2 e are in 2px orbital

2 e are in 2py orbital

2 e are in 2pz orbital

Electronic configuration

No of e in sub

shell

Electronic configuration of shell

1s2

2s22p6

3s23p63d10

4s24p64d10

4f14

2

10

6

14

10

2

2

6

6

2

Rules of electronic configuration of atom

• Each e shell can hold max. 2n2 electrons

• Pattern of e entering in shell:

1 2 3 4 5 6 7

• Pattern of e entering in subshell:

s p d f

• Entering of e in orbital/ Hund’s rule:

Electrons are distributed among the orbitals of a subshell in such a way as to give the max. number of unpaired e and have the same direction of pair

Aufbau or Building up rule

Electrons tend to occupy the available orbitals in increasing order of energies, the orbital of lower energy being filled first. This is building up/Aufbau principle

•The energy of an orbital is determined by the sum of principle quantum number (n) & the angular quantum number (l), this is (n+l) rule

•If in case of two orbital having the same (n+l) value, the orbital with with lower value of n has lower energy.

Rules of electronic configuration of atom

(n+l) rule

The relation between orbital filling and the periodic table

Write electron configuration of the following elements

• O (8) = ?

• K (19) = ?

• Cl (17) = ?

• Fe (26) = ?

• Zn (30) = ?

• Pb (82) = ?

Electron configurations in the first three periods.

Orbital occupancy for the first 10 elements, H through Ne.

Hund’s rule

A periodic table of partial ground-state electron configurations

Assignment 1Assignment 1• Questions number 5, 9, 12, 16 & 23 to 33.

• Among these 14 questions answer any 7 questions

• Clearly write your name & ID no in the front cover of your assignment sheet

• You can submit the assignment in hand written or as printed form, as you like

• Last date of submission of Assignment 1 is November 15, 2008.

• If anyone submit the Assignment 1 before November 8, 2008 then he/she will be given Bonus 2 marks at the final

• If anyone answers all 14 questions correctly and submit his/her Assignment copy then he/she will be rewarded with Bonus 5 marks at the final

SuggestionSuggestion: Please prepare your notes at least according to Please prepare your notes at least according to the question banks, you can show me your notes, if any the question banks, you can show me your notes, if any correction needed or suggestion then I can give you that.correction needed or suggestion then I can give you that.