An electron in an atom is known to be in a state with magnetic quantum number. What is the smallest possible value of the principal quantum number of the state?

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Each electron in an atom is characterized by four numbers that arise from the resolution of Schrödinger's equations. These numbers are called quantum numbers. Each energy level corresponds to a main known quantum number, which is represented by the letter n. This number gives an idea of the location of an energy level with respect to the nucleus. The higher n, the mayor will be the energy of that level and the farther away from the nucleus is removed.

In each energy level there may be sub-levels. Each of them is specified by another quantum number called secondary, specified with the letter l. The value of this quantum number can vary from zero to n-1. For example, in the first energy level, the quantum number can only take a value that is zero, while in the second level, it can take a value between zero or one. Then, it can be said that the values of the quantum number n indicate the size of the orbital, that is, its proximity to the nucleus; and the values of the quantum number l variables the orbital:

• If l = 0, the orbital is of type s.

• If l = 1, the orbitals are of type p.

• If l = 2, the orbitals are of type d.

• If l = 3, the orbitals are of type f.