quantum mechanichal model2

7/27/2019 Quantum Mechanichal Model2

1/14


2/14

Objectives:

1) Define the orbital

2) Describe all the 4 quantum numbers ofan electron in an orbital:

i. principal quantum number, n

ii. Angular momentum quantum number, l

iii. Magnetic quantum number, m

iv. Electron spin quantum number, s


3/14

AtomicOrbital

An orbital is a three-dimensional region inspace around the nucleus

where there is a highprobability of finding anelectron.

Definition


4/14

QUANTUM NUMBER

Each of the electrons in an atom isdescribed and characterised by a setof four quantum numbers, namely

a) principal quantum number, n

b) angular momentum quantum number, l

c) magnetic quantum number, m

d) electron spin quantum number, s.


5/14

Principle Quantum Number(n )

n= 1, 2, 3, 4, ,

2.2

Indicates the energy level of aspecific electron also known shell

The

principal quantum number mayhave only integral values:


6/14


7/14


8/14

Angular Momentum Quantum Number, l

Letters are assigned to different numerical values ofl.

Numericalvalue ofl Symbol

0

1

2

3

Orbital shape

s

p

d

f

spherical

dumbbell

cloverleaf


9/14

Angular Momentum Quantum Number, l

- lis dependant on n. (i.e., 0 l< n).Value of n Value ofl Subshells

1 0 1s

2 0,1 2s, 2p

3 0,1,2 3s,3p,3d

4 0,1,2,3 4s,4p,4d,4f


10/142.2

l= 2 (d orbitals)

l= 0 (s orbital) l= 1 (p orbital)

l= 2 (d orbitals)l= 2 (d orbital)


11/14

for a given value of l

m= -l,., 0, . +l

~is orientation of the orbital in space

ifl= 1 (p orbital), m = -1, 0, or1

ifl= 2 (d orbital), m= -2, -1, 0, 1, or2

Magnetic Quantum Numberm

2.2


12/14

Exercise

Shell nl

(l


13/14

Electron Spin Quantum Number, s

The value ofs determines the direction of spinningmotions of an electron (either clockwise or counterclockwise) which is spinning on its own axes, as Earthdoes.

The electron spin quantum number has a value of+

1

2-

1

2or


14/14

PrincipleQuantumNumber,

n (shell)

AngularMomentum(subshell)

Subshelldsgntn

MegneticQuantumNumber, l

Electronspin

quantumnumber,

s

No. oforbitals

in

subshell

Numberof

electron

1 0 1s 0 1 2

20 2s 0 1

81 2p -1, 0, +1 3

3

0 3s 0 1

181 3p -1, 0, +1 3

2 3d-2, -1, 0, +1,

2 5

4

0 4s 0 1

32

1 4p -1, 0, +1 3

2 4d-2, -1, 0, +1,

2 5

3 4f-3, -2, -1, 0,

+1, 2, 3 7

n 2n2

Table 1: The four quantum numbers of electron.

quantum mechanichal model2

Documents