At what temperatures rms velocity, average velocity & most probable velocity of `O_(2)` molecules will be 1500 `m*s^(-1)`?

Explanation

Molar mass (M) of `O_(2)=32g*mol^(-1)=0.032kg*mol^(-1)`
In case of rms velocity`:(3RT_(1))/(M)=(1500)^(2)`
or, `(3xx8.314xxT_(1))/(0.032)=(1500)^(2) or, T_(1)=2886.697K`.
In case of average velocity: `(8RT_(2))/(piM)=(1500)^(2)`
or, `(8xx8.314xxT_(2))/(0.032xx3.14)=(1500)^(2) or, T_(2)=3399.085K`.
In case of most probable velocity: `(2RT_(3))/(M)=(1500)^(2)`
or, `(2xx8.314xxT_(2))/(0.032xx3.14)=(1500)^(2) or, T_(3)=4330.045K`.