Which of the following is not a possible de-Broglie's wavelength of a particle, which moves inside a cubical box of side length L, without losing any energy (elastically colliding with walls of cube)?
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a
b
c
d
All of these
answer is D.
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Detailed Solution
Using concept of stationary waves, we can say at rigid walls Node formation takes place.L=λ2, λ, 3λ2, 2λ..., nλ2 where n=1,2,3... Longest wavelength is specified by λ=2L. next by λ=Lthen λ=L×23. etc In general λn=2Ln,n=1,2,3,…For(a) λ=2L3For (b) λ=LFor (c) )λ=2L . Hence, all are possible.