The rms velocity of `CO_(2)` at a temperature, T (in kelvin) is x `eras^(1)`. At what temperature (in kelvin), the rms velocity of nitrous oxide would be 4 x `ems^(-1)`? (Atomic weights of C, N and O are 12, 14 and 16 respectively),

Options

A. 16 T
B. 2T
C. 4T
D. 32 T

Answer

a

Explanation

rms velocity of `CO_(2), V_(rms) (CO_(2)) =s sqrt((3RT_(CO_(2)))/M_(CO_(2)))`
` V_(rms) (CO_(2)) =sqrt((3RT_(CO_(2)))/M_(CO_(2)))`
rms velocity of `N_(2)O, V_(rms) (N_(2)O) = sqrt((3RT_(N_(2)O))/M_(N_(2)O))`
` (V_(rms)(CO_(2)))/ (V_(rms)(N_(2)O))=sqrt(T_(CO_(2))/T_(N_(2)O))`
Squaring on both the sides, we get,
` X^(2)/(16X^(2))= T_(CO_(2))/T_(N_(2)O)`
` therefore T_(N_(2)O)=16T`