The root mean square velocity of one mole of a monoatomic gas having molar mass M is Urms. The relation between average kinetic energy (E) of the gas and Urms is :
A
Urms=√3E2M
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B
Urms=√2E3M
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C
Urms=√2EM
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D
Urms=√E3M
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Solution
The correct option is CUrms=√2EM The root mean square velocity of one mole of a monoatomic gas having molar mass M is Urms. The relation between average kinetic energy (E) of the gas and Urms is Urms=√2EM The root mean square velocity of one mole of a monoatomic gas is given by the following expression. Urms = √3RTM......(1) The average kinetic energy (E) of the gas is given by the following expression. E=32RT RT=23E......(2) Substitute (2) into (1) Urms =
⎷3×23EM Urms = √2EM Hence, the option (C) is the correct answer.