1.

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

Answer»

<P>`(3.87h)/(m_(0)c)`
`(4.92h)/(m_(0)c)`
`(7.57h)/(m_(0)c)`
`(9.46h)/(m_(0)c)`

Solution :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)`


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