Question

Quantum numbers arise naturally from the mathematics used to describe the possible states of an electron in an atom. The four quantum numbers, the principal quantum number (n), the angular momentum quantum number (â), the magnetic quantum number (mâ), and the spin quantum number (ms) have strict rules which govern the possible values. Identify allowable combinations of quantum numbers for an electron. Select all that apply.

n = 4, â= 0, mâ= 1, ms= 1/2
n = 3, â= â2, mâ= â1, ms= â1/2
n = 5, â= 3, mâ= 1, ms= 1/2
n = 3, â= 3, mâ= 0, ms= 1/2
n = 2, â= 1, mâ= 0, ms= 0
n = 3, â= 2, mâ= â1, ms= 1/2

Answer 1

n = 3, â= 2, mâ= â1, ms= â1/2

n = 5, â= 3, mâ= 1, ms= 1/2

Explanation:

Quantum numbers are used to describe an electron in an atom. According to Pauli exclusion theory, no two electrons in an atom has the same value for all four quantum numbers.

For, n = 3, â= 2, mâ= â1, ms= â1/2

The n=3 level can have values of azimuthal quantum number 0,1,2

Where l=2, the values of the magnetic quantum number are -2,-1,0,1,2

The spin quantum number must be ±1/2

Hence this option is a possible combination.

For n = 5, â= 3, mâ= 1, ms= 1/2

The n=5 level may have azimuthal quantum numbers 0,1,2,3.

For l=3, the values of magnetic quantum number are; -3,-2,-1,0,1,2,3

The spin quantum number must be ±1/2

Hence this option is a possible combination.