Consider hypothetical situation. We have a one dimensional box of length L with perfectly reflecting walls. Photons as well as electrons can be present in the box if they form standing waves with nodes at the end. The photon can be only completely absorbed by electron if it can go to a higher excited state. An electron can go from higher excited state to lower excited state only if it emits photons which can form standing wave in the box. Select correct $$option(s)$$. Take $$hmeLc=1(c$$: speed of the light, me : mass of the $$electron)$$:

Question

Consider hypothetical situation. We have a one dimensional box of length L with perfectly reflecting walls. Photons as well as electrons can be present in the box if they form standing waves with nodes at the end. The photon can be only completely absorbed by electron if it can go to a higher excited state. An electron can go from higher excited state to lower excited state only if it emits photons which can form standing wave in the box. Select correct $$option(s)$$. Take   $$hmeLc=1(c$$: speed of the light, me : mass of the $$electron)$$:

Infinity Learn · Accepted Answer

nλ$$2=L$$​$$Ephoton=hc$$λ$$=hnc2L=mec2n2$$​$$Eelectron=p22me=h$$λ$$22me=mec28n2Option$$ $$1$$ : If electron jumps from $$n=1$$ to $$n=3$$, it will require $$energy=mec2832$$−$$12=mec2$$​This energy can be given by a photon in its $$2nd$$ harmonic.Option $$3$$ : An electron in $$2nd$$ excited state can go from $$n=3$$ to $$n=1$$​Energy released by $$electron=mec2832$$−$$12=mec2$$​which matches with energy of photon in $$2nd$$ harmonic.Option $$4$$ : An electron in $$5th$$ excited state can go from $$n=6$$ to $$n=4$$​Energy released by $$electron=mec2862$$−$$42=52mec2$$​which matches with energy of photon in $$5th$$ harmonic.

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