Initially, the root mean square (rms) velocity of N2 molecules at certain temperature is u. If this temperature is doubled and all the nitrogen molecules dissociate into nitrogen atoms, then the new rms velocity will be :

Question

Initially, the root mean square (rms) velocity of N2 molecules at certain temperature is u. If this temperature is doubled and all the nitrogen molecules dissociate into nitrogen atoms, then the new rms velocity will be : (A) u / 2 (B) 2u (C) 4u (D) 14u

Tardigrade Admin · Accepted Answer

v = √(3RT/2 (n)0) v' = √(3R×2T/14) (v/v') = √(1/4) (v/v') = (1/2) v' = 2v

Q. Initially, the root mean square (rms) velocity of $N_{2}$ molecules at certain temperature is u. If this temperature is doubled and all the nitrogen molecules dissociate into nitrogen atoms, then the new rms velocity will be :

$u /2$

$2 u$

$4 u$

$14 u$

$v = \frac{3 RT}{2 \frac{n}{0}}$
$v^{'} = \frac{3 R \times 2 T}{14}$
$\frac{v}{v ^{'}} = \frac{1}{4}$
$\frac{v}{v ^{'}} = \frac{1}{2}$
$v^{'} = 2 v$

Q. Initially, the root mean square (rms) velocity of N2​ molecules at certain temperature is u. If this temperature is doubled and all the nitrogen molecules dissociate into nitrogen atoms, then the new rms velocity will be :

u/2

2u

4u

14u