Question

how does the energy of an electron change when the electron moves closer to the nucleus

Answer 1

Under what conditions? Generally speaking, and certainly if it's in a stationary state (like being in a 1s orbital), it's energy wouldn't change, since energy is generally conserved. What *would* happen is that its potential energy would decrease, due to the attraction between the nucleus and the electron, and its kinetic energy would increase (it would speed up) to compensate.

If what you mean is, what would happen if an electron moved to a lower energy stationary state, e.g. an electron in a 2s orbital emits a photon and drops to a 1s orbital, which puts it on average closer to the nucleus, then the answer of course is that its energy decreases. In general stationary (stable) states of the electron that are closer to the nucleus have less energy.

Answer 2

energy of electron in nth orbit is given by
En=-13.12/ n^2 kj/mol^-1
energy of an electron can be calculated using this formula. where n=principle quantum no.[1,2,3.........]
so as electron goes to higher principal shell 'n' increases and hence 'En' decreases as it is inversly proportional to square of 'n' and vice versa.