Find de Broglie wavelength of neutron at `127^(@)C` Given, Boltzmann constant, `k = 1.38 xx 10^(-23) J.mol^(-1).K^(-1)`, Planck's constant, `h = 6.626 xx 10^(-34)J.s`, mass of neutron, `m = 1.66 xx 10^(-27) kg`

Explanation

Kinetic energy of neutron `E = (3)/(2) k T`
We know, `E = (1)/(2) mv^(2) or, 2Em = m^(2) v^(2)`
or, `mv = sqrt(2Em) = sqrt(2m xx (3)/(2) kT) = sqrt(3mkT)`
`:.` de Broglie wavelength,
`lamda = (h)/(mv) = (h)/(sqrt(3mkT))`
`= (6.626 xx 10^(-34))/(sqrt(3 xx 1.66 xx 10^(-27) xx 1.38 xx 10^(-23) xx 400))`
`= 1.264 xx 10^(-10) m`