Question

Which of the following represent a valid set of quantum numbers?
n = 1, l = 0, ml = -1, ms = +1/2
n = 3, l = 2, ml = -2, ms = -1/2
n = 2, l = 2, ml = -1, ms = +1/2
n = 2, l = 1, ml = 0, ms = 0
n = 2, l = 1, ml = 0, ms = -1/2

Answer 1

Among the above mentioned options, only 2 options represent valid set of quantum numbers.

n = 3, l = 2, ml = -2, ms = -1/2

n = 2, l = 1, ml = 0, ms = -1/2

The three coordinates that come from Schrodinger's wave equations are the principal (n), angular (l), and magnetic (m) quantum numbers. These quantum numbers describe the size, shape, and orientation in space of the orbitals on an atom.

• The principal quantum number (n) cannot be zero. The allowed values of n are therefore 1, 2, 3, 4, and so on.
• The angular quantum number (l) can be any integer between 0 and n - 1. If n = 3, for example, l can be either 0, 1, or 2.
• The magnetic quantum number (m) can be any integer between -l and +l. If l = 2, m can be either -2, -1, 0, +1, or +2.
• The magnetic spin can be of +1/2 or -1/2.

Therefore in the above options, no.1 is not valid i.e. n = 1, l = 0, ml = -1, ms = +1/2.

reason: ml value is not according to the rule -l to +l.

Option no.3 is not valid i.e.n = 2, l = 2, ml = -1, ms = +1/2.

reason: value of l should be from 0 to n-1.

Option no. 4 is not valid. i.e. n = 2, l = 1, ml = 0, ms = 0.

reason: the magnetic spin can not be 0.

therefore based on the above explainations, we can say that options 2 and 5 are correct. i.e.

n = 3, l = 2, ml = -2, ms = -1/2

n = 2, l = 1, ml = 0, ms = -1/2