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The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T (Kelvin) and mass mₙ is:

1. h / √3mₖT
2. 2h / √3mₖT
3. 2h / √mₖT
4. h / √mₖT

Correct answer: h / √3mₖT

Solution

The de-Broglie wavelength is given by λ = h / p, where p is the momentum. For a neutron in thermal equilibrium, its kinetic energy is (3/2)kT, so p = √(2mₙ(3/2)kT). Substituting this into the de-Broglie formula gives λ = h / √(3mₙkT).

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