The temperature at which the root mean square velocity of `SO_(2)` molecules is same as that of `O_(2)` molecules at `27^(@)C`

Options

A. `327^(@)C`
B. 327 K
C. `32.7^(@)C`
D. 32.7 K

Answer

A

Explanation

For `O_(2)` r.m.s. `= (3RT)/(M) = sqrt((3R xx 300)/(32))`
For `SO_(2)` r.m.s. `= sqrt((3RT)/(64))`
Since both the velocities are same
`:. Sqrt((3RT)/(64)) = sqrt((3 R xx 300)/(32))`
Solving, `T = 600 K`
`:. T = 600 - 273 = 327^(@)C`