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

The de Broglie wavelength of an atom at absolute temperature T will be ______. (m = mass of the atom, k_B = Boltzmann constant)

Asked in GUJCET 2015 · Matter waves in other settings

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

Step-by-step solution

Why the other options are wrong

• (2) Drops the square root: mk_BT is not a momentum (it equals (p²)/3), and h/(mk_BT) has the unit s kg⁻¹, not metres.
• (3) Upside down: p/h is 1/λ, with unit m⁻¹. It also takes K = k_BT instead of the mean translational energy 3/2k_BT.
• (4) This is a momentum, √2mK with K = k_BT; with no h in it, it cannot be a wavelength.

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