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  • When Root mean squares velocity of Nitrogen molecules in a container at particular Temperature is  <img alt="\mathrm{\left(1+\frac{8}{x}\right) \frac{1}{2} \times v}" src="https

When Root mean squares velocity of Nitrogen molecules in a container at particular Temperature is 

\mathrm{\left(1+\frac{8}{x}\right) \frac{1}{2} \times v}, When V is average speed of molecule. Find the value of 'x' \mathrm{(\pi \approx 3)}

Option: 1

46


Option: 2

64


Option: 3

32


Option: 4

36


Answers (1)

best_answer

\mathrm{\begin{aligned} & V_{\text {rms }}=\sqrt{\frac{3 R T}{M}}, \quad V_{\text {ang }}=\sqrt{\frac{B R T}{\pi m}} \\ & \sqrt{\frac{3 R T}{m}}=\left(1+\frac{\theta}{x}\right)^{\frac{1}{2}} \cdot \sqrt{\frac{\partial R T}{\pi m}} \end{aligned}}

squaring both side

\mathrm{\begin{aligned} & \frac{3 R T}{m}=\left(1+\frac{8}{x}\right) \times \frac{8 R T}{\pi} m \\ & \frac{3}{8} \pi=1+\frac{8}{x} \quad(\pi \approx 3) \\ & \frac{9}{8}-1=\frac{8}{x} \\ & \frac{1}{8}=\frac{8}{x} \\ & x=64 \end{aligned}}

Posted by

seema garhwal

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