(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If the Maxwell-Boltzmann distribution of energy is f(E)=2*pi*E^{1/2}*(1/pi*k*T)^{3/2}*e^{E/kT}. Can you calculate the most probable energy from this? (The answer is kt/2).

2. Relevant equations

Some kind of integration (guassian integral) is needed from 0 to infinity I believe.

3. The attempt at a solution

I tried integration by parts and some other methods with no luck. My teacher made it clear that this is not a gamma function (my initial thought since the E^{1/2}is paired with an exponential function) and that the answer is relatively easy. Any help would be much appreciated!

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# Calculate most probable energy from Maxwell-Boltzmann distribution of energy

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