The actual ground state of atomic calcium Z20 is 1s22s22p63s

The actual ground state of atomic calcium (Z=20) is 1s22s22p63s23p64s2

a. In a universe where the electron had spin s = 5/2, what would the ground state of calcium be?

b. In a universe where the electron had spin s = 0, what would the ground state of calcium be?

Solution

Calcium has 20 electrons to distribute.

(a) when s = 5/2 => multiplicity of each state = 2s+1 = 6 (instead of 2 as in the case of s = 1/2)

now the

s-shell can hold = 6 electron

and

p-shell can hold = 18 electron

so the configuration of calcium would have been,

1s⁶ 2s⁶ 2p⁸

(b) when s = 0 => multiplicity of each state = 2s+1 = 1

now the

s-shell can hold = 1 electron

p-shell can hold = 3 electron

and

d-shell can hold = 5 electron

so the configuration of calcium would have been,

1s¹ 2s¹ 2p³ 3s¹ 3p³ 4s¹ 3d⁵ 4p³ 5s¹ 4d¹