Question

Which one of the following sets of quantum numbers represents an electron with the highest energy?

A) n = 3, l = 2, ml = -2, ms = +1/2 D) n = 5, l = 0, ml = 0, ms = +1/2
B) n = 4, l = 1, ml = 0, ms = -1/2 E) n = 4, l = 2, ml = -1, ms = -1/2
C) n = 4, l = 0, ml = 0, ms = +1/2

Answer 1

The correct answer is option D) n = 5, l = 0, ml = 0, ms = +1/2.

Step-by-step explanation:

When looking for the electron with the highest energy, we examine the principal quantum number (n), angular momentum quantum number (l), magnetic quantum number (ml), and spin quantum number (ms).

The principal quantum number (n) primarily determines the energy level and, generally, a higher 'n' means a higher energy level. Next, within a given principal energy level, the angular momentum quantum number (l) determines the shape of the orbital, and a higher 'l' contributes to higher energy within that level. Both ml and ms provide further subdivision of energy states, but they do not directly affect the energy ranking as much as 'n' and 'l' do. Given that, the highest energy electron will be the one with the highest values of 'n' and 'l'.

Comparing the given sets of quantum numbers, the electron represented by D) n = 5, l = 0, ml = 0, ms = +1/2 has the highest principal quantum number and, consequently, the highest energy. Despite having an l value of 0, the high principal quantum number of 5 indicates that it is on the highest energy level among the given options.