Question

The temperature at which the rms speed of oxygen molecules becomes equal to the rms speed of hydrogen molecules at 300 K is

• A. 4800 K
• B. 2400 K
• C. 1200 K
• D. 600 K
• E. 300 K

Hint:

For equal RMS speeds: \[ \frac{T_1}{M_1}=\frac{T_2}{M_2} \] This shortcut saves time.

Answer 1

The Correct Option is A

RMS speed is: \[ v_{\text{rms}}=\sqrt{\frac{3RT}{M}} \] For oxygen at temperature \(T\): \[ v_{\text{rms,O}_2}=\sqrt{\frac{3RT}{32}} \] For hydrogen at \(300\text{ K}\): \[ v_{\text{rms,H}_2}=\sqrt{\frac{3R(300)}{2}} \] Given both are equal: \[ \sqrt{\frac{3RT}{32}}=\sqrt{\frac{3R(300)}{2}} \] Squaring both sides: \[ \frac{T}{32}=\frac{300}{2} \] \[ T=32\times \frac{300}{2}=16\times 300=4800\text{ K} \]
Hence, the correct answer is: \[ \boxed{(A)\ 4800\text{ K}} \]