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

Answer 1

Answer: (D)

450 K

Answer 2

$\frac{U_{MP}}{U_{rms}} = \sqrt{\frac{\frac{2RT_{1}}{M}}{\frac{3RT_{2}}{M}}} = \sqrt{\frac{2}{3}\frac{T_{1}}{T_{2}}} \Rightarrow \frac{2}{3}\frac{T_{1}}{T_{2}} = 1$

$T_{1} = \frac{3}{2} \times 300 = 450K$