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Physics321
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Homework Statement
What is the de Broglie wavelength of a neutron whose kinetic energy is equal to the average kinetic energy of a gas of neutrons at temperature T = 17 K?
Homework Equations
lambda = h/p = h/mv.
The Attempt at a Solution
Well first I tried taking the h = 6.63E-34 Jxs and dividing it by the mass times the square root of T = 17 K
Thus,
(6.63E-34)/(1.6E-27 kg)(sqrt(17)) x (1E9 m) = 100.500 nm.
I did this because we know from kinetic theory that T is proportional to the root mean square velocity v in the gas, so that v scales as sqrt(T). This means that the momentum scales in the same way, while the wavelength as 1/sqrt(T).
I'm not sure where to go from here, since the answer is not correct. =/