Kinetic theory of gases theory question

[Mandavi]

Homework Statement

Consider a mixture of oxygen and hydrogen kept at room temperature.As compared to a hydrogen molecule an oxygen molecule hits the wall-
(a) with greater average speed
(b)with smaller average speed
(c)with greater average kinetic energy
(d)with smaller average kinetic energy

Homework Equations

We have to consider both the gases as ideal to get the answer.
Now, for a mixture v_rms=(3RT/M)^1/2
where M is average mass of the gases in the mixture and is
M=(n₁M₁+n₂M₂)/n₁+n₂
n denote the number of moles of gases and M their respective molecular masses.
Average kinetic energy for a gas molecule=3/2kT
k=boltzmann constant
T=absolute temperature

The Attempt at a Solution

The answer given is (b)with smaller average speed.Someone please explain the reason for this.

 

[Dweirdo]

If I understood it right :
both molecules have the same average internal energy, which is kinetic energy
now,the oxygen molecule is heavier than the hydrogen molecule , thus the velocity of the oxygen molecule should be smaller.
mv^2/2 = E
V=(3RT/M)^1/2 when the mass is higher . velocity is lower...

 

[Mandavi]

If I understood it right :
both molecules have the same average internal energy, which is kinetic energy
now,the oxygen molecule is heavier than the hydrogen molecule , thus the velocity of the oxygen molecule should be smaller.
mv^2/2 = E
V=(3RT/M)^1/2 when the mass is higher . velocity is lower...

Right,but doesn't the word "average" has any significance here?

 

[Dweirdo]

I would rather say Energy per molecule.
the "Average" thing is here because this measures the average velocity ,but it has (if it has) a little effect on the answer. the difference between 2 different types of molecules in this case is big, so you can drop that word.

 

[Mandavi]

I would rather say Energy per molecule.
the "Average" thing is here because this measures the average velocity ,but it has (if it has) a little effect on the answer. the difference between 2 different types of molecules in this case is big, so you can drop that word.

Okay!Thank you very much!