Question

A sample of helium gas contains 50 atoms, following table gives number of molecules ($N$) moving with definite speed ($v$); rms (root mean square) speed of sample is approximately
$\begin{array}{cccccc}v& 6.0& 8.0& 9.0& 11.0& 13.0\\ N& 10& 16& 11& 9& 4\end{array}$

• A. $9m/s$
• B. $18m/s$
• C. $4m/s$
• D. $15m/s$

Answer 1

The correct option is A $9m/s$

Rather than solving, we can eliminate from option as rms value will lie between lowest (6) and highest value (13). So, answer should be $9m/s$.

If not solved from option elimination then it will be solved by-
$v_{rms}=\sqrt{\frac{\sum v^2}{N}}$
$=\sqrt{\frac{{10.6}^2+{16.8}^2+{11.9}^2+{9.11}^2+{4.13}^2}{50}}$
$=\sqrt{\frac{360+1024+891+1089+676}{50}}=\sqrt{80.8}$
$\approx 9m/s$