The Total solution for NCERT class 6-12
(a) For what kinetic energy ofa neutron will the associated de Broglie wavelength be 1.40 × 10−10 m?
(b) Also find the deBroglie wavelength of a neutron, in thermal equilibrium with matter, having anaverage kinetic energy of (3/2) kT at 300 K.
(a) De Brogliewavelength of the neutron, λ = 1.40 × 10−10 m
Mass of a neutron, mn =1.66 × 10−27 kg
Planck’s constant, h = 6.6× 10−34 Js
… (1)
Using equation (2) inequation (1), we get:
Hence, the kinetic energy of the neutron is6.75 × 10−21 J or 4.219 × 10−2 eV.
(b) Temperature of theneutron, T = 300 K
Boltzmann constant, k =1.38 × 10−23 kg m2 s−2 K−1
Average kinetic energy ofthe neutron:
The relation for the deBroglie wavelength is given as:
Therefore,the de Broglie wavelength of the neutron is 0.146 nm.