Question

The quantum numbers of six electrons are given below. Arrange them in order of increasing energies. If any of these combination(s) has/have the same energy lists:

1. n = 4, l = 2, m_l = –2 , m_s = - 1/2
2. n = 3, l = 2, m_l= 1 , m_s = +1/2
3. n = 4, l = 1, m_l = 0 , m_s = +1/2
4. n = 3, l = 2, m_l = –2 , m_s = –1/2
5. n = 3, l = 1, m_l = –1 , m_s= +1/2
6. n = 4, l = 1, m_l = 0 , m_s = +1/2

Answer 1

For n = 4 and l = 2, the orbital occupied is 4d.

For n = 3 and l = 2, the orbital occupied is 3d.

For n = 4 and l = 1, the orbital occupied is 4p.

Hence, the six electrons i.e., 1, 2, 3, 4, 5, and 6 are present in the 4d, 3d, 4p, 3d, 3p, and 4p orbitals respectively.

Therefore, the increasing order of energies is 5(3p) < 2(3d) = 4(3d) < 3(4p) = 6(4p) < 1 (4d).

Answer 2

The orbitals occupied by the electrons are:

(1) 4d

(2) 3d

(3) 4p

(4) 3d

(5) 3p

(6) 4p

Same orbitals will have same energy and higher the value of (n+l) higher is the energy,
Their energies will be in order: (5) < (2) = (4)< (6) = (3) < (1).