de-Borglie wavelength of particle moving at a `(1^(th))/(4)` od speed of light having rest mass `m_(0)` is….

Options

A. `(3.87h)/(m_(0)c)`
B. `(4.92h)/(m_(0)c)`
C. `(7.57h)/(m_(0)c)`
D. `(9.46h)/(m_(0)c)`

Answer

A

Explanation

de-Broglie wavelength `lambda=(h)/(p)=(h)/(mv)`
but m=`(m_(0))/(sqrt(1-(v^(2))/(v^(2)))`
`lambda=(h(sqrt(1-v^(2)//c^(2))))/(m_(0)c)`
Now `v=(c )/(4)`
`lambda=(hsqrt(1-(c^(2))/(16c^(2))))/(m_(0)c//4)=(hsqrt(((16c^(2)-c^(2)))/(16c^(2))))/(m_(0)c//4)`
`sqrt((15)/(16)h)/(m_(0)c//4)=(4xx0.968h)/(m_(0)c)`
`lambda =(3.87h)/(m_(0)c)`