Thermal neutron spectrum

[sandon]

The most probable velocity of thermal neutrons can than be approximated by the Boltzmann constant and is given by the following:

v = sqrt (2kT/m)

where
k is the Boltzmann constant
T is the temperature
m is the mass of the neutrons

My question is why is the above equation not the following

v= sqrt(3kT/m)

 

[sandon]

Dont need an answer i got it

 

[raining Pete]

The equation v = sqrt(2kT/m) is derived from the kinetic theory of gases, where it is assumed that particles move in a random, chaotic motion. This motion can be described by the root-mean-square (RMS) velocity, which is the average velocity of particles in a gas. The RMS velocity is given by the following equation:

v_rms = sqrt(3kT/m)

However, in the case of thermal neutrons, they have a specific type of motion called thermal motion or thermal agitation. This motion is not completely random and can be described by the Maxwell-Boltzmann distribution, which takes into account the specific properties of neutrons.

The Maxwell-Boltzmann distribution gives the most probable velocity of particles in a gas, which is represented by the peak of the distribution curve. In the case of thermal neutrons, this most probable velocity is given by the equation:

v_mp = sqrt(2kT/m)

This is the reason why the equation v = sqrt(2kT/m) is used for thermal neutrons, instead of v = sqrt(3kT/m). The latter is more appropriate for particles with completely random motion, while the former takes into account the specific properties of thermal neutrons.