What is the temperature at which oxygen molecules have the same r.m.s. velocity as the hydrogen molecules at `27^(@)C`-

Options

A. `3527^(@)C`
B. `4227^(@)C`
C. `4527^(@)C`
D. `4000^(@)C`

Answer

C

Explanation

r.m.s. velocity `C = sqrt(( 3RT)/( M))`
For oxygen `Co_(2) = sqrt(( 3RT)/( 32))`
For `CH_(2) ` at `27^(@)C =sqrt(( 3xxR xx300)/( 2))`
When `Co_(2) = CH_(2)`
`sqrt(( 3RT)/( 32)) = sqrt (( 3 xx R xx 300)/( 2))`
`( 3RT)/( 32) = ( 3R xx 300)/( 2)`
`T= ( 300 xx 32)/( 2) = 4800K` < br> Then in `""^(@) C T= 4800 - 273 = 4527^(@)C`