The root mean square velocity of one mole of a monoatomic
gas having molar mass M is uᵣ.ₘ.ₛ.. The relation between the
average kinetic energy (E) of the gas and uᵣ.ₘ.ₛ. is
(a) uᵣ.ₘ.ₛ. = √3E/2M
(b) uᵣ.ₘ.ₛ. = √2E/3M
(c) uᵣ.ₘ.ₛ. = √2E/M
(d) uᵣ.ₘ.ₛ. = √E/3M
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answer : option (c) uᵣ.ₘ.ₛ = √{2E/M }
The root mean square velocity of one mole of a monoatomic gas having molar mass M is uᵣ.ₘ.ₛ
root mean square is given by, uᵣ.ₘ.ₛ = √{3RT/M}......(1)
where T is temperature in Kelvin and M is molecular weight of gas.
also we know, translational kinetic energy of gas, E = 3RT/2 ......(2)
putting equation (2) in equation (1) we get,
uᵣ.ₘ.ₛ = √{2/M {3RT/2} = √{2/M × E}
= √{2E/M}
hence, option (c) is correct choice.
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