The de - Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature `T ("kelvin")` and mass `m`, is

Options

A. `h/sqrt(3mkT)`
B. `(2h)/sqrt(3mkT)`
C. `(2h)/sqrt(mkT)`
D. `(h)/sqrt(mkT)`

Answer

A

Explanation

Kinetic energy of a neutron in thermal equilibrium with heavy at a temperature T is given as
`K-3/2 T " "...(i)`
Also momentum (p) is `p=sqrt(2mk)`
From eqn(i)
`p=sqrt(2m.(3)/2kT)=sqrt(3mkT)`
Required de - Broglie wavelength is given as
`lamda=h/p=h/(sqrt(3mkT))`