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Suppose we have an electron of $\rm{H}$ atom( suppose it is at 4th shell). But it can't remain in the excited state for a long time. So it can jump to 1st ,2nd or the 3rd orbital. What is the factor that decides whether the electron will jump to any one of the lower energy state orbitals. Or is that random?

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It is random, to some extent, but the probability of transition can be calculated (with some approximations).

The most usual one is the electric dipole approximation, which is clearly dominant. The probability is proportional to $\langle \phi_{final} | \vec{r} | \phi_{initial} \rangle$

This also makes some transitions impossible. That's why we do not observe all "possible" spectral lines, but only some combinations. The rules that tell what ones are possible transitions are called *selection rules*.

This is caused by the dominant term (electric dipole), but you can consider magnetic dipoles, or quadrupoles... but their contribution is of much less significance.

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  • $\begingroup$ Einstein once said,"God doesn't play dice." Is that random or we don't know the answer. $\endgroup$ – Sujal Koirala Sep 26 '18 at 13:34
  • $\begingroup$ Hawking replied "Not only does God definitely play dice, but He sometimes confuses us by throwing them where they can't be seen". Haha. $\endgroup$ – FGSUZ Sep 26 '18 at 13:44
  • $\begingroup$ Okay, seriously, that's a good question, but it is beyond the scope of physics. Are things really random? We just can't tell, or at least not yet. The thiing is that considering things random works, so it is a nice model. We just aren't able to control every tiny force on every tiny particle at every single instant. It's a dead end, but don't worry, simplified models work. Wether things (things in general) are really random or not, that might be more philosophy than physics, at least until we disconver something different. $\endgroup$ – FGSUZ Sep 26 '18 at 13:47

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