Q.

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):
 

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a

An electron in state n = 1 can go to n = 3

b

A photon corresponding to 4th harmonic can be emitted by an electron in 5th excited state.

c

A photon corresponding to 2nd harmonic can be emitted by an electron in 2nd excited state.

d

A photon corresponding to 5th harmonic can be emitted by an electron in 5th excited state.

answer is A, C, D.

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Detailed Solution

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nλ2=LEphoton=hcλ=hnc2L=mec2n2Eelectron=p22me=hλ22me=mec28n2

Option 1 :If electron jumps from n=1 to n=3, it will require energy=mec283212=mec2This 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=1Energy released by electron=mec283212=mec2which matches with energy of photon in 2nd harmonic.

Option 4 :An electron in 5th excited state can go from n=6 to n=4Energy released by electron=mec286242=52mec2which matches with energy of photon in 5th harmonic.

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