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

At equilibrium thermal energy possessed by neutron `= (3)/(2) kT`
`lambda = (h)/(p) = (h)/(sqrt(2mE)) = (h)/(sqrt(2m(3)/(2)kT))`
`lambda = (h)/(sqrt(3m k T))`