Question

how does the energy of an electron change when the electron moves closer to the nucleus?
it stays the same.
it increases.
it doubles.
it decreases.

Explanation:

When an electron moves closer to the nucleus, it moves to a lower - energy orbital. This is because electrons in orbitals closer to the nucleus are more strongly attracted to the positively - charged nucleus, and the energy of an electron in an atom is related to its distance from the nucleus. The formula for the energy of an electron in a hydrogen - like atom is \(E =-\frac{Z^{2}e^{4}m}{8\epsilon_{0}^{2}h^{2}n^{2}}\) (where \(Z\) is the atomic number, \(e\) is the elementary charge, \(m\) is the electron mass, \(\epsilon_{0}\) is the vacuum permittivity, \(h\) is Planck's constant, and \(n\) is the principal quantum number). As \(n\) (which is related to the distance of the electron from the nucleus) decreases (electron moves closer), the magnitude of \(E\) increases (but since \(E\) is negative, the actual energy value becomes more negative, meaning the energy decreases).

Answer:

It decreases.