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A particle of mass is confined to a narr...

A particle of mass is confined to a narrow tube of length L.
(a) Find the wavelengths of the de-Brogile wave which will resonate in the tube.
(b) Calculate the corresponding particle moments. and
(c) Calculate the corresponding energies.

Text Solution

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(a)The de-Broglie waves will resonate with a node at each end of the tube.

A few of the possible resonance forms are as follows :
`lambda_n="2L"/n, n=1,2,3`……

(b)Since de-Broglie wavelengths are `lambda_n=h/p_n`
`p_n=h/lambda_n`
`="nh"/"2L"`, n=1,2,...

(c ) The kinetic energy of the particles are `K_n=p_n^2/"2m"`

`=(n^2h^2)/(8L^2m) n=1,2,3`......
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