Question

when an electron moves from a lower to a higher energy level, the electron
moves closer to the nucleus.
absorbs a continuously variable amount of energy.
always doubles its energy.
absorbs a quantum of energy.

Explanation:

When an electron moves from a lower to a higher energy level, it needs to absorb energy. According to quantum theory, the energy levels are quantized. So the electron absorbs a specific amount (a quantum) of energy. Moving closer to the nucleus would mean a lower energy level (as the electrostatic attraction is stronger closer to the positively - charged nucleus). Energy absorption is not a continuously variable amount (as energy levels are discrete in atoms) and there is no rule that it always doubles its energy.

Answer:

absorbs a quantum of energy.