How many electrons in an atom can have each of the following quantum number or sublevel designations?

(a) n = 2, l = 1, ml = 0

(b) 5p

(c) n = 4, l = 3

Answer: (a) 2 (b) 6 (c) 14

Explanation:

In the Azimuthal quantum number (l) electrons in a particular subshell (such as s, p, d, or f) are defined by values of l (0, 1, 2, or 3).

s is l=0, p is l=1, d is l=2, f is l=3.

The magnetic quantum number (ml) The value of ml can range from - l to + l, including zero. Thus the s, p, d, and f subshells contain 1, 3, 5, and 7 orbitals each, with values of m within the ranges 0, ±1, ±2, ±3 respectively. Each shell can have 2 x l + 1 sublevels, and each of these sublevel can accommodate up to two electrons.

(a) n=2, l=1, ml=0. If l=1 then 2 x 1 + 1=3 sublevels, 3*2=6 electrons. When l=1, ml = -1,0,+1, ml=0 accommodate two (2) electrons

(b) 5p. p is l=1 If l=1 then 2 x 1 + 1=3 sublevels, 3*2 = electrons. This means in the 5 shell, the p orbital has 3 subshell and accommodate 6 electrons.

(c) n = 4, l = 3 if l=3 then 2 x 3 + 1=7 sublevel 7*2=14 electrons. This means the in the 4 shell, the f orbital has 7 subshell and accomdate 14 elections.