Assume a gas of molecular mass M g/molecule obeys the Maxwell Boltzmann distribution of speeds at temperature T. If u2> u1, the ratio of the number of molecules at speed u2 to the number at speed u1

a) is always less than one.
b) is always greater than one.
c) can be either greater than one or less than one.
d) will decrease if the temperature increases for fixed m.
e) will not change if mass m increases for fixed T.

Is this a comparison of KE to KE?

The answer is C but not sure why so

To answer this question, we need to understand the Maxwell-Boltzmann distribution and how it relates to the speeds of gas molecules at a given temperature.

The Maxwell-Boltzmann distribution describes the distribution of speeds of gas molecules in a system at a given temperature. It states that at a particular temperature T, the probability of a gas molecule having a certain speed u is given by:

P(u) = 4π( M / (2πRT))^(3/2) * u^2 * exp(-M*u^2 / (2RT))

where M is the molecular mass of the gas molecule, R is the ideal gas constant, and exp denotes the exponential function.

Now, let's consider the scenario mentioned in the question where u2 > u1. We want to compare the number of molecules at speed u2 to the number at speed u1.

To do this, we can compare the probabilities of having speeds u2 and u1 respectively, at a given temperature T. Let's call these probabilities P(u2) and P(u1).

The ratio of the number of molecules at speed u2 to the number at speed u1 can be calculated using the following formula:

(P(u2) / P(u1)) = [(u2^2 / u1^2) * exp(-(M/2RT)*(u2^2 - u1^2))]

Now, let's analyze the given answer choices:

a) is always less than one.

Since the ratio formula above involves the ratio of speeds raised to the power of 2, and exponentials of negative values, it is unlikely that the ratio will be always less than one.

b) is always greater than one.

Similar to option a, it is unlikely that the ratio will always be greater than one.

c) can be either greater than one or less than one.

The most plausible answer is c, since the ratio will depend on the specific values of u2 and u1, as well as the molecular mass M, the temperature T, and the gas constant R. By plugging in values, we can determine whether the ratio is greater than or less than one.

d) will decrease if the temperature increases for fixed M.

This answer choice is incorrect because the ratio of the number of molecules at different speeds does not depend solely on the temperature T. It also depends on the speeds u2 and u1, as well as the molecular mass M.

e) will not change if mass M increases for fixed T.

This answer choice is incorrect because the ratio will indeed be affected by a change in the molecular mass M. The ratio formula explicitly contains the molecular mass M in the exponential term.

In conclusion, the correct answer is c) can be either greater than one or less than one.