Explain Aufbau Principle with example

The electrons, identified by quantum numbers n and l,

(i) n = 4, l = 1,

(ii) n = 4, l = 0,

(iii) n = 3, l = 2, and

(iv) n = 3, l = 1

can be placed in order of increasing energy, from the lowest to highest, as:

(A) (iv) < (ii) < (iii) < (i) (B) (ii) < (iv) < (i) < (iii)

(C) (i) < (iii) < (ii) < (iv) (D) (iii) < (i) < (iv) < (ii)

Energy of an orbital, increases with the sum of Principal quantum number (n) and azimuthal Quantum

Number (n + l).

If the sum value two orbitals are same (n + l), then, among them one with lowest ‘n’, value will have

the lower energy.

Energy of the orbitals will then be –

 

Principal Quantum Number =n =

Azimuthal quantum Number = l =

n + l =

i

4

1

5

ii

4

0

4

iii

3

2

5

iv

3

1

4

 

 Orbitals ii) and iv) has lowest (n + l) of 4. So, they are of lower energy than i) and iii).

 Among ii) and iv), the latter has minimum ‘n’. So, iv has the lowest energy followed by ii).

 Among higher energy i) and iii) having the same (n + l) value of 5, iii) has low ‘n’ value and has lower energy than i).

 The orbitals then can be arranged in the increasing energy order as iv) < ii) < iii) < i)

As per the order the correct choice is ‘A’

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