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Consider a hydrogen atom, to excite the electron to a higher orbit, it should interact with photons of energy equal to that of the energy difference between the two states.

If the energy of photon is lesser, the electron rises up to an unstable stated above which it can't rise. After that out falls back to the initial stage letting the photon emit.

If the energy of that photon is higher then the electron rises to a stable higher level and even above that. The electron finally falls back to the stable higher state giving the additional energy in the form of a photon of very small wave length.

But I found that the electron excites if only the energy matches. I'm not able to resolve this in any of the lectures.

What restricts excitation of electron with a photon of higher energy?

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The probability of atomic excitation by photon absorption is given in terms of the "cross- section" for single photon absorption. This quantity shows a sharp peak if the photon energy and the atomic energy level difference match (the coupling between the atom and electromagnetic field causes the atomic states to broaden, the natural line width). Thus excitation by photons of higher energy is possible but its probability is very small.

However, using high intensity lasers it is possible, depending on selection rules, to excite through the absorption of multiple photons with the sum of their energies equal to the atomic level difference. In fact it is even possible to ionize an atom in this way (multi-photon ionisation).

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    $\begingroup$ Can you please add the graph for probability of Atomic excitation vs the photon energy and the atomic energy level difference. $\endgroup$ – ryanafrish7 Nov 15 '14 at 12:23
  • $\begingroup$ I do not know that by heart but am confident that an internet search will be successful. $\endgroup$ – Urgje Nov 15 '14 at 12:43
  • $\begingroup$ I looked for it on the internet and I'm unable to find a one. $\endgroup$ – ryanafrish7 Nov 15 '14 at 14:26
  • $\begingroup$ Indeed, to my surprise I did not find it either. It is one of the oldest subjects in atomic spectra and should be given in some data base. I only found some general books:springer.com/physics/… maximumbook.org/… barnesandnoble.com/w/… Maybe you could try a new post about this. $\endgroup$ – Urgje Nov 16 '14 at 12:32
  • $\begingroup$ Please reply me on this comment on finding a post relevant to my question $\endgroup$ – ryanafrish7 Nov 16 '14 at 14:11

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