Question

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

1) n = 4, l = 0, ml = 0, ms = 1/2
2) n = 3, l = 2, ml = -2, ms = 1/2
3) n = 5, l = 0, ml = 0, ms = 1/2
4) n = 4, l = 1, ml = 0, ms = -1/2
5) n = 4, l = 2, ml = -1, ms = -1/2

Answer 1

The set of quantum numbers with the highest energy is {n = 5, l = 0, ml = 0, ms = 1/2}, as the principal quantum number (n) is the most influential in determining base energy levels for electrons.

Step-by-step explanation:

To determine which set of quantum numbers represents an electron with the highest energy, we must understand the role of each quantum number. The principal quantum number (n) has the largest effect on the electron's energy: the larger the value of n, the higher the energy level of the electron. The angular momentum quantum number (l) also adds to the energy but to a lesser extent, and it is limited to values ranging from 0 up to n - 1. The magnetic quantum number (ml) and spin quantum number (ms) do not directly affect the energy of the electron in the absence of an external magnetic or electric field.

With this understanding, we can see that the set of quantum numbers representing the highest energy electron is {n = 5, l = 0, ml = 0, ms = 1/2}. This is because it has the highest principal quantum number (n) among the options provided. Though the values of l, ml, and ms do influence energy under certain conditions, the principal quantum number is the most influential in determining base energy levels.