A diamtomic gas consisting of rigid molecules is at a temperature of `87^(@)C`. If the moment of inertia is `2.76 xx 10^(-39) gcm^(2)`, then the rms angular speed of the molecule is (Boltzmann constant `= 1.38 xx 10^(-23)JK^(-1)`)

Options

A. `6 xx 10^(12) rads^(-1)`
B. `3 xx 10^(12) rads^(-1)`
C. `6 xx 10^(13) rads^(-1)`
D. `3 xx 10^(13) rads^(-1)`

Answer

A

Explanation

Moment of inertia of diatomic molecule,
`I = (2)/(3) Mr^(2)`
So, radius, `r = sqrt((3I)/(2M))`…(i)
rms speed of molecule,
`v = sqrt((3kT)/(M))` rms angular speed,
`omega = (v)/(r ) = (sqrt(3kT//M))/(sqrt(3I//2M)) = sqrt((2kT)/(I))`
`= sqrt((2 xx 1.38 xx 10^(-23) xx (87 + 273))/(2.76 xx 10^(-46)))`
`= sqrt(360 xx 10^(23)) = sqrt(36 xx 10^(24))`
`=6 xx 10^(12) rad//s`