Question

Suppose a gas sample in all hace $6\times {10}^{23}$ molecule . Each ${1/3}^{rd}$ of the molecules have rms speed ${10}^{4}cm/sec$ and ${2\times 10}^{4}cm/sec$ and ${3\times 10}^{4}cm/sec$. Calculate the rms speed of gas molecules in sample.

Answer 1

• Out of $6\times {10}^{23}$ molecules, $2\times {10}^{23}$ molecules have rms speed ${10}^{4}cm/s$, $2\times {10}^{23}$ molecules have rms speed $2\times {10}^{4}cm/s$ and $2\times {10}^{23}$ molecules have rms speed $3\times {10}^{4}cm/s$.
  
• The rms speed of gas sample can be calculated as,

$v_{rms}=\sqrt{\frac{\left[2\times {10}^{23}\times ({10}^4{)}^2\right]+\left[2\times {10}^{23}\times (2\times {10}^4{)}^2\right]+\left[2\times {10}^{23}\times (3\times {10}^4{)}^2\right]}{6\times {10}^{23}}}$

$v_{rms}=\sqrt{\frac{14\times {10}^8}{3}}=2.16\times {10}^{4}cm/s$