The de-Broglie wavelength of a neutron corresponding to root mean square speed at `927^(@)`C is `lambda` What will be the de-Broglie wavelength of the neutron corresponding to root mean square speed at `27^(@)`

Options

A. `(lambda)/(2)`
B. `lambda`
C. `2 lambda`
D. `4 lambda`

Answer

C

Explanation

`K.E.` of neutron `E=(3)/(2)KT`
`lambda_(d)=(h)/(p)=(h)/(sqrt(2mE))=(h)/(sqrt(2mxx(3)/(2)kT))`
`rArr lambda_(2)=lambdasqrt(((927+273))/(27+273))= 2 lambda`