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The ratio between RMS velocities of H(2)...

The ratio between RMS velocities of `H_(2)` at 50 K and `O_(2)` at 800 K is

A

`4 : 1`

B

`2 : 1`

C

`1: 1`

D

`1: 4 `

Text Solution

Verified by Experts

The correct Answer is:
C
Root mean square speed = `sqrt(3RT)/(M)`
Given, `M_(1)` = molar mass of ` H_(2) = 2 `
`M_(2)`= molar mass of `O_(2) = 32`
`T_(1) = 50 K, T_(2) = 800` K
On taking ratio of `r_(1) and r_(2)`, we get
`(r_(1))/(r_(2)) = sqrt((M_(2) xx T_(1))/(M_(1) xx T_(1))) = sqrt((32)/(2)) xx sqrt((T_(1))/(T_(2)))`
`(r_(1))/(r_(2)) = sqrt(16) xx sqrt((50)/(800)) or (r_(1))/(r_(2)) = 4 xx (1)/(4)`
or `" " (r_(1))/(r_(2)) = (1)/(1) = 1: 1 `
hence, option (c ) is correct.
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