The wavelength of de Broglie waves associated with a thermal neutron of mass m at absolute temperature T is given by (k is the Boltzmann constant)

Options

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

Answer

C

Explanation

`E = (3)/(2) kT`, again, `E= (1)/(2) mv^(2) = ((mv)^(2))/(2m)`
or, `mv = sqrt(2mE) = sqrt(2m.(3)/(2)kT) = sqrt(3mkT)`
`:.` de Broglie wavelength, `lamda = (h)/(mv) = (h)/(sqrt(3mkT))`