In an atom, the principal quantum number (n) determines the:

Quantum numbers are a set of four numbers that describe the position and energy of an electron in an atom. The principal quantum number, written n, is the first of them. It can take only positive whole-number values: n = 1, 2, 3, 4 and so on. These values correspond to the main shells, which are also named K, L, M, N and so on.

As the value of n increases, the electron is, on average, farther from the nucleus. So the shell, and the orbital, becomes larger, and its energy becomes higher (less negative). This is why n is said to decide the size and the energy of the orbital. In a hydrogen atom, the energy of the electron depends only on n.

The principal quantum number also tells us how many orbitals and electrons a shell can hold. The number of orbitals in a shell is n squared, and the maximum number of electrons is 2n squared. So the K shell (n = 1) holds 2 electrons, the L shell (n = 2) holds 8, the M shell (n = 3) holds 18 and the N shell (n = 4) holds 32.

The four quantum numbers are:

• Principal (n): size and energy of the orbital.
• Azimuthal or subsidiary (l): shape of the orbital; values 0 to (n–1), giving the s, p, d and f subshells.
• Magnetic (m or ml): orientation of the orbital in space; values from –l to +l.
• Spin (s or ms): direction of the electron's spin; +½ or –½.

Why not the other options?

• ✗The shape of the orbital is decided by the azimuthal quantum number l.
• ✗The orientation of the orbital is decided by the magnetic quantum number m.
• ✗The spin of the electron is described by the spin quantum number s.