Q140 / 160 · TS EAMCET 2016 · Physics

Uranium has two isotopes of masses 235 and 238 wits. If both of them are present in wranium hexafluoride gas, find the percentage ratio of difference in rms velocities of two isotopes to the rms velocity of heavier isotope.

  • A
    1.64
  • B
    0.064
  • Correct answer
    C
    0.64
  • D
    6.4

Solution

Given, Mass of first uranium isotope $=238$ units Mass of second uranium isotope $=235$ units We know that, $$ \begin{aligned} & v_{\text {rms }} & =\sqrt{\frac{\gamma R T}{M}} \\ \Rightarrow & v_{\text {rms }} & \propto \frac{1}{\sqrt{M}} \end{aligned} $$ So, the percentage ratio of difference in rms velocity of isotopes is given by $$ \begin{aligned} & \frac{V_{\mathrm{rms}_2}-V_{\mathrm{rms}_1}}{V_{\mathrm{rms}_2}} \times 100 \\ & =\frac{\sqrt{M_1}-\sqrt{M_2}}{\sqrt{M_1}} \times 100 \\ & =\frac{\sqrt{238}-\sqrt{235}}{\sqrt{238}} \times 100 \end{aligned} $$ $$ \begin{aligned} & =\frac{15.427-15.329}{15.427} \times 100=\frac{0.097}{15.427} \times 100 \\ & =6.34 \times 10^{-3} \times 100=0.634 \approx 0.64 \end{aligned} $$

Hence, the correct answer is option: 'C'.

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