Suppose an electron in the 2nd shell gets excited and jumps to the 4th shell. Shouldn't the electron then exist in an unstable equilibrium in the 4th shell, than lose energy and drop down to the 2nd shell? What causes it to come out of the equilibrium position and lose energy? The teacher who gave me this problem to think about said that quantum mechanics plays a role in this. Can anyone please give an explanation?
Actually, this question is not as bad as the comments may make you think. It's actually quite a sensible question, because when we solve the usual, Schrödinger's equation-based, QM problem of energy states of hydrogen atom (or any other atom), we get eigenstates of the Hamiltonian we inserted into the equation. These solutions should thus be stable for infinite time.
In real world, however, an atom isn't isolated. It interacts with the electromagnetic field, and this interaction results in spontaneous emission, which is the reason why an atom can't be in excited state indefinitely.
The energy here is a kind of potential energy. By very nature, it always tries to stay minimum in magnitude, so it is said to have a "potential" to change its energy into other form of energy. Like stretch bow's potential energy change into (and transferred to) arrow's kinetic energy. in case of electron jumps, the energy transformed is in the form light.