Question

Which of the following has zero spin and angular momentum?
A.$Ca_{20}^{40}$
B.$H_1^3$
C.$C_6^{14}$
D.$Cl_{17}^{37}$

Answer 1

The spin is the intrinsic momentum of the electron and is purely a quantum mechanical phenomenon. The orbital angular momentum is due to the revolution of the electron around the nucleus of the atom. The atom with no unpaired electron will have zero spin.

Complete step by step solution:
In $Ca_{20}^{40}$ , the calcium atom has 20 protons and 20 electrons arranged as: $1{s^2}2{s^2}2{p^6}3{s^2}3{p^6}4{s^2}$. So it can be seen that each electron is paired in its orbital and hence, the calcium atom has zero spin.
In the $H_1^3$, the tritium atom has 1 electron in its valence shell and hence, it is clear that its spin is unbalanced.
In $C_6^{14}$, the carbon atom has 14 electrons arranged as such: $1{s^2}2{s^2}2{p^2}$ and according to Hund’s rule as there are three p orbitals, so the two electrons will each occupy of the orbitals “p” first. Hence, the spin momentum is not zero here.
In $Cl_{17}^{37}$, the chlorine atom has 17 electrons, arranged as such: $1{s^2}2{s^2}2{p^6}3{s^2}3{p^5}$. Hence, in any one of the p orbital, one electron remains unpaired and hence the spin remains unbalanced.

So, the only atom with a balanced spin is the calcium atom. So, the correct option is A.

Note:
According to Pauli's exclusion principle, no two electrons can have the same set of all four quantum numbers, and that is why the spins of two electrons in the same orbital are different, one is clockwise, while the other is counter clockwise. In this the magnetic moments of the electrons they balanced.