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?
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5$\begingroup$ Why does a stone fall to the ground, rather than just sit comfortably in the air? $\endgroup$– Ivan NeretinCommented Oct 9, 2019 at 19:15
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4$\begingroup$ In order for the excited state to decay it needs to be perturbed. An excited isolated system in vacuum can decay to a lower state by spontaneous emission which is caused by the fact that on very short times scales the vacuum is not empty. The energy-time uncertainty locally allows for large energies in a short time. In fact, so much energy that a electron-positron pair can be formed and annihilated during this short time. These vacuum fluctuations induce the decay. $\endgroup$– PaulCommented Oct 9, 2019 at 19:45
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5$\begingroup$ @IvanNeretin I don't think that's the right picture. After all, one could instead ask 'why does a stone fall off the mountain, rather than staying at the peak?'. The answer is that in fact they don't spontaneously fall off the peak—some can rest there for centuries or more; to fall, they need to be perturbed. $\endgroup$– theoristCommented Oct 10, 2019 at 0:02
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4$\begingroup$ en.wikipedia.org/wiki/Spontaneous_emission $\endgroup$– Buck Thorn ♦Commented Oct 10, 2019 at 7:48
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$\begingroup$ @theorist - see Phosphorescence // Forbidden transitions shouldn't occur, but do so because of perturbations. $\endgroup$– MaxWCommented Mar 8, 2020 at 20:17
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2 Answers
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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.
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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.
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$\begingroup$ As Ivan Neretin has also hinted at the concept with another example of potential energy $\endgroup$– AdityaCommented Oct 9, 2019 at 19:35