Question

Calculate the de Broglie wavelength of a neutron having kinetic energy of 150 eV.

Answer 1

Given: K = 150 eV

Mass of neutron = 1.675 × 10⁻²⁷ kg

Planck’s constant (h) = 6.63 × 10⁻³⁴ Js

Formula: de Broglie wavelength:

`λ = h/p`

For non-relativistic particles:

`λ = h/sqrt(2 m K)`

Convert energy to joules

1 eV = 1.6 × 10⁻¹⁹ J

K = 150 × 1.6 × 10⁻¹⁹ J

= 2.4 × 10⁻¹⁷ kg

`λ = h/sqrt(2 m K)`

= `(6.63 xx 10^-34)/sqrt(2 xx 1.67 xx 10^-27 xx 2.4 xx 10^-17)`

= `(6.63 xx 10^-34)/sqrt(8.016 xx 10^-44)`

= `(6.63 xx 10^-34)/(2.83 xx 10^-22)`

= 2.34 × 10⁻¹² m