Find the initial momentum of electron if...

Find the initial momentum of electron if the momentum of electron is changed by `p_(m)` and the De Brogile wavelength associated with it changed by `0.50%`

Text Solution

Verified by Experts

`(dlambda)/(lambda) xx 100 = 0.5 rArr (dlambda)/(lambda) = (0.5)/(100) = (1)/(200)` and `Deltap = p_(m)`
`:' p = h/lambda`, differenting `(dp)/(dlambda) = -(hc)/(lambda^(2)) = - (hc)/(lambda) xx 1/(lambda) = - (p)/(lambda) rArr (|dp|)/(p) = (dlambda)/(lambda)`
`:. (p_(m))/(p) = (1)/(200) rArr p = 200 p_(m)`

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The angular momentum of p electron is

`(h)/(2pi)sqrt(6)`

`h sqrt(2)`

`(h)/(2pi)sqrt(2)`

`hsqrt(6)`

If the momentum of an electron is changed by Delta p , then the de - Broglie wavelength associated with it changes by 0.50 % . The initial momentum of the electron will be

`(Delta p)/(200)`

`(Delta p)/(199)`

`199 Delta p`

`400 Delta p`

The kinetic energy of an electron gets tripled, then the de-Broglie wavelength associated with it changes by a factor

`1/3`

`sqrt(3)`

`(1)/(sqrt(3))`