Question:
The wavelength of light from the spectral emission line of sodium is 589 nm. Find the kinetic energy at which (a) an electron, and (b) a neutron, would have the same de Broglie wavelength.
Answer:
Wavelength of light of a sodium line, 
= 589 nm 
m
Mass of an electron, me
kg
Mass of a neutron, mn=
kg
Planck’s constant, h
Js
(a) For the kinetic energy K, of an electron accelerating with a velocity v, we have the relation:
We have the relation for de Broglie wavelength as:
Substituting equation (2) in equation (1), we get the relation:
Hence, the kinetic energy of the electron is 
J or 4.31
.
(b) Using equation (3), we can write the relation for the kinetic energy of the neutron as:
Hence, the kinetic energy of the neutron is 
J or 2.36 neV.
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