Practice portal › Dual Nature of Matter and Radiation › Comparing de Broglie Wavelengths of Particles

The de Broglie wavelength of a neutron of mass m in thermal equilibrium with heavy water at a temperature T (in kelvin) is:

Asked in NEET 2017 · Matter waves in other settings

• (1) h/(√3mkT)
• (2) (2h)/(√3mkT)
• (3) (2h)/(√mkT)
• (4) h/(√mkT)

Step-by-step solution

Why the other options are wrong

• (2) comes from carries a stray factor of two: substituting K=3/2kT into p=√2mK cancels the 2 exactly, leaving √3mkT with nothing in front of it
• (3) comes from combines both of the other slips, a leftover factor of two together with a thermal energy of 1/2kT instead of 3/2kT
• (4) comes from uses 1/2kT for the neutron's energy, which is the share belonging to one degree of freedom; a free neutron moves in three dimensions and carries 3/2kT

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