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WBJEE · Chemistry · States of Matter

Let \(\left(\mathrm{C}_{\mathrm{rms}}\right)_{\mathrm{H}_2}\) is the r.m.s speed of \(\mathrm{H}_2\) at \(150 \mathrm{~K}\). At what temperature, the most probable speed of helium \(\left[\left(\mathrm{C}_{\mathrm{mp}}\right)_{\mathrm{He}}\right]\) will be half of \(\left(\mathrm{C}_{\mathrm{rms}}\right)_{\mathrm{H}_2}\) ?

  1. A \(75 \mathrm{~K}\)
  2. B \(112.5 \mathrm{~K}\)
  3. C \(225 \mathrm{~K}\)
  4. D \(900 \mathrm{~K}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(112.5 \mathrm{~K}\)

Step-by-step Solution

Detailed explanation

\(C_{\mathrm{rms}}=\sqrt{\frac{3 R T}{M}} \quad C_{m p}=\sqrt{\frac{2 R T}{M}}\) As per question \(\frac{1}{2} \sqrt{\frac{3 \times R \times 150}{2}}=\sqrt{\frac{2 R T}{4}}\) \(\mathrm{T}=112.5 \mathrm{~K}\)