SID: 440617329 ..
Question 1
1a)
1b)
Question 2
2a)
Please see attachment
2b)
Full working in attachment under 2a)
, where x = , u =
2c)
We see that the 2D distrobution has a lower most likely speed at v = u/sqrt(2) compared to v = u for the 3D case.
Both have the same most likely velocity vector of 0.
Both distrobution amplitudes increase as we increase x, indicating the larger multiplicites of vectors available at higher speeds.
However, after the peak likely speed, the probability amplitudes begin to fall (with skewed right tails) as the increasing multiplicity of available vector states for a given speed is compeonsated by fact that the probability of obtaining any such invididual vector decays exponentially with increasing speed.
2d)
Please see attachment
2e)
Please see attachment
Question 3
Let x = kT/ep
Noting that 0 is parity even
3a)
3b)
3c)
3d)
Just for a nice figure
Question 4
Please see attachment