Question

How many electrons could be held in the second shell of an atom if the spin quantum number ms could have three values instead of just two?

a. 2

b. 6

c. 8

d. 12

Answer 1

If the spin quantum number ms had three possible values, the second shell of an atom could hold 12 electrons because of the additional capacity provided by the extra spin state.

Step-by-step explanation:

To determine how many electrons the second shell of an atom can hold if the spin quantum number had three values instead of two, we refer to the Pauli exclusion principle, which states that no two electrons can have the same set of quantum numbers within an atom. Normally, the second shell has one s subshell (which can hold 2 electrons) and three p orbitals (each of which can hold 2 electrons), so it can contain 2(2(1)+1) + 3(2(1)+1) = 2 + 6 = 8 electrons. If each of these orbitals could hold an additional electron due to a third spin state, we would multiply the number of orbitals by three, resulting in 1(3) for the s subshell, and 3(3) for the p orbitals, thus, 3 + 9 = 12 electrons in total.