At what temperature the rms speed of oxygen atom equal to rms speed of helium gas atom at `-10^(@)C`?
Atomic mass of helium = 4
Atomic mass of oxygen = 32

Explanation

Here,
`V_(rms)=[(3PV)/(M)]^((1)/(2))=[(3RT)/(M)]^((1)/(2))`
Let rms speed of oxygen is `(V_(rms))_(1)`, and of helium is `(V_(rms))_(2)` is equal at temperature `T_(1)` and `T_(2)` respectively.
`((V_(rms))_(1))/((V_(rms))_(2))=sqrt((M_(2)T_(1))/(M_(1)T_(2)))`
Atomic mass of Helium `M_(2)=4`
Atomic mass of Oxygen `M_(1)=32`
Temperature of helium `-10^(@)C=273+(-10^(@)C)`
`=273-10`
= 263 K
`[(4T_(1))/(32xx263)]=1,T_(1)=(32xx263)/(4)=(8416)/(4)=2104K`
`therefore T_(1)=2104K`