The V_rms of gas molecules is 300 m/sec. If its absolute temperature is reduced to half and molecular weight is doubled the V_rms will become:

CONCEPT: 

• Gas Molecules are in Constant Motion.
• Root mean Square Speed: The root mean square speed of Gas average of roots of the speed of all Gas molecules present in the given volume.

It is given as 

R = Gas Constant

T = Absolute Temperature of Gas 

M = Molecular Weight of Gas

CALCULATION:

Given V_^rms = 300m/s. 

Let, initial Absolute Temperature is T and initial Molecular weight be M. So,

 .......  (1)

Now, the Absolute Temperature is halved, So the new absolute Temperature T' = T/2

Also, Molecular weight is doubled, So the new molecular weight M' = 2M

The New root mean square speed

 .................. (2)

Putting the values of T' and M' in Equation (2) we get

⇒ ............  (3)

Comparing Equation (3) and Equation (1)

⇒ V'rms = 300 m/s / 2 = 150 m/s

So, 150 m/s is the Answer.

So, Option 2 is correct.

Additional Information

• The Average of all speeds of the Gas molecule is given as

• The Speed passed by the maximum fraction of the total number of molecules, or most probable speed is given as: