Question

What does a set of four quantum numbers tell you about an electron? Compare and contrast the locations and properties of two electrons with quantum number sets (4, 3, 1, +½) and (4, 3, -1, +½).

Answer 1

The principal quantum number, n, designates the principal electron shell. Because n describes the most probable distance of the electrons from the nucleus, the larger the number n is, the farther the electron is from the nucleus, the larger the size of the orbital, and the larger the atom is. n can be any positive integer starting at 1, as n=1 designates the first principal shell (the innermost shell). The first principal shell is also called the ground state.

The orbital angular momentum quantum number l determines the shape of an orbital, and therefore the angular distribution. The number of angular nodes is equal to the value of the angular momentum quantum number l. The value of l is dependent on the principal quantum number n. Unlike n, the value of l can be zero. It can also be a positive integer, but it cannot be larger than one less than the principal quantum number (n-1):

for s orbital l=0, for p l=1, for d l=2, for f l=3

The magnetic quantum number m determines the number of orbitals and their orientation within a subshell. Consequently, its value depends on the orbital angular momentum quantum number ll. Given a certain l, m is an interval ranging from -l to +l, so it can be zero, a negative integer, or a positive integer.

Unlike n, l, and m, the electron spin quantum number s does not depend on another quantum number. It designates the direction of the electron spin and may have a spin of +1/2, represented by↑, or –1/2, represented by ↓. This means that when s is positive the electron has an upward spin, which can be referred to as "spin up." When it is negative, the electron has a downward spin, so it is "spin down." The significance of the electron spin quantum number is its determination of an atom's ability to generate a magnetic field or not.