Two molecules of a gas have speeds of 9 times | vedclass

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Question

(C) The root mean square $(v_{rms})$ speed for $n$ molecules is given by the formula:$v_{rms} = \sqrt{\frac{v_{1}^{2} + v_{2}^{2} + \dots + v_{n}^{2}}

Vedclass · Accepted Answer

$6.40 	imes 10^{6} \ m/s$

Vedclass · Answer

(C) The root mean square $(v_{rms})$ speed for $n$ molecules is given by the formula:$v_{rms} = \sqrt{\frac{v_{1}^{2} + v_{2}^{2} + \dots + v_{n}^{2}}{n}}$For two molecules,the formula becomes:$v_{rms} = \sqrt{\frac{v_{1}^{2} + v_{2}^{2}}{2}}$Given:$v_{1} = 9 	imes 10^{6} \ m/s$$v_{2} = 1 	imes 10^{6} \ m/s$Substituting the values:$v_{rms} = \sqrt{\frac{(9 	imes 10^{6})^{2} + (1 	imes 10^{6})^{2}}{2}}$$v_{rms} = \sqrt{\frac{81 	imes 10^{12} + 1 	imes 10^{12}}{2}}$$v_{rms} = \sqrt{\frac{82 	imes 10^{12}}{2}}$$v_{rms} = \sqrt{41 	imes 10^{12}}$$v_{rms} = \sqrt{41} 	imes 10^{6} \ m/s$Since $\sqrt{41} \approx 6.403$,$v_{rms} \approx 6.40 	imes 10^{6} \ m/s$

Two molecules of a gas have speeds of $9 \times 10^{6} \ m/s$ and $1 \times 10^{6} \ m/s$ respectively. What is the root mean square speed of these molecules?

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