Question

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

Explanation:

When an electron moves from a lower to a higher energy level, it requires energy. According to quantum theory, electrons absorb discrete amounts (quanta) of energy for such transitions. Moving closer to the nucleus would mean lower energy (since energy levels increase with distance from the nucleus in a simple model). The energy change is not always a doubling (depends on specific energy levels). Also, in quantum mechanics, the energy absorbed is not a continuously variable amount (energy levels are quantized).

Answer:

absorbs a quantum of energy.