At what temperature most probable speed of O2 molecules have the same value of root mean square speed of O2 molecules at 300 K ?

Question

At what temperature most probable speed of O2 molecules have the same value of root mean square speed of O2 molecules at 300 K ? (A) 150 K (B) 600 K (C) 750 K (D) 450 K

Tardigrade Admin · Accepted Answer

(UMp/Urms)=√((2RT1/M)/(3RT2)M) =√(2T1/3T2) ⇒ (2/3) (T1/T2)=1 T1=(3/2)×300=450 K

Q. At what temperature most probable speed of $O_{2}$ molecules have the same value of root mean square speed of $O_{2}$ molecules at $300 K$ ?

$150 K$

$600 K$

$750 K$

$450 K$

$\frac{U _{Mp}}{U _{r m s}} = \frac{\frac{2 R T _{1}}{M}}{\frac{3 R T _{2}}{M}}$
$= \frac{2 T _{1}}{3 T _{2}}$
$\Rightarrow \frac{2}{3} \frac{T _{1}}{T _{2}} = 1$
$T_{1} = \frac{3}{2} \times 300 = 450 K$

Q. At what temperature most probable speed of O2​ molecules have the same value of root mean square speed of O2​ molecules at 300K ?

150K

600K

750K

450K