Question

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

Answer 1

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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