Question

The wavelength of light from the spectral emission line of sodium is $589 \,nm$. The kinetic energy at which a neutron would have the same de Broglie wavelength is

• A. $3.81 \times 10^{-28} J$
• B. $3.81 \times 10^{-25} J$
• C. $4.81 \times 10^{-28} J$
• D. $4.81 \times 10^{-30} J$

Answer 1

Answer: (A)

Given, wavelength of light $=589 \,nm =589 \times 10^{-9}\, m$
Mass of electron $m _{ e }=9.1 \times 10^{-31}\, kg$
Mass of neutron $m _{ n }=1.67 \times 10^{-27}\, kg$
Planck's constant $h =6.62 \times 10^{-34}\, J - s$
Kinetic energy of neutron
$ KE _{ n }=\frac{ h ^2}{2 \lambda^2 m _{ n }} $
$=\frac{\left(6.63 \times 10^{-34}\right)^2}{2 \times\left(589 \times 10^{-9}\right)^2 \times 1.66 \times 10^{-27}} $
$=3.81 \times 10^{-28} \,J$