Question

The ratio between the rms Speed of H2 at 50K and that of O2 at 800K is :

Answer 1

U1:U2 = T1×M2 : T2: M1

U1:U2= 50×32: 800×2

U1:U2= 1:1

Answer 2

Answer: The ratio will be 1.

Explanation:

The formula used for root mean square speed is:

$\nu_{rms}=\sqrt{\frac{3RT}{M}}$

where,$\nu_{rms}$ = root mean square speed

R = gas constant

T = temperature = 50 K

M = atomic mass of hydrogen = 2 g/mole

Now put all the given values in the above root mean square speed formula, we get:

$\nu_{rms}=\sqrt{\frac{3\times R\times 50}{2}$

2) For rms of $O_2$ at 800 K.

$\nu_{rms}=\sqrt{\frac{3RT}{M}}$

where,

$\nu_{rms}$ = root mean square speed

R = gas constant

T = temperature =800 K

M = atomic mass of oxygen = 32 g/mole

Now put all the given values in the above root mean square speed formula, we get:

$\nu_{rms}=\sqrt{\frac{3\times R\times 800}{32}$

The ratio between the rms speed of $H_2$ at 50K and that of $O_2$ at 800K is $\frac{(\frac{3\times R\times 50}{2})}{(\frac{3\times R\times 800}{32})}=1$

Hence, the ratio is 1.