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Question

The root mean square speed of a gas molecule is 300 m/s. What will be the root mean square speed of the molecules if the atomic mass is doubled and absolute temperature is halved?

A
300 m/s
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B
150 m/s
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C
600 m/s
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D
175 m/s
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Solution

The correct option is B 150 m/s
Given:
Initial root mean square speed, vrms=300 m/s
To find:
Final root mean square speed when the atomic mass is doubled and absolute temperature is halved, vrms=?

We know that,
vrms=3RTM, where M is molar mass and T is absolute temperature.
300=3RTM .......(1)
Now, if molar mass is doubled and absolute temperature is halved, then
vrms=3RT/22M=3RT4M=123RTM
vrms=3002 [ from (1) ]
vrms=150 m/s

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