Correct Answer - Option 1 : H
2
Concept:
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Root Mean Square Speed: It is defined as the square root of the mean of squares of the speed of different molecules.
- The root-mean-square speed takes into account both molecular weight and temperature, two factors that directly affect the kinetic energy of a material.
From the expansion of pressure,
\(P = \frac{1}{3}{\rm{\rho v}}_{rms}^2\)
\({v_{rms}} = \sqrt {\frac{{3P}}{\rho }} \)
\(V_{rms}= \sqrt {\frac{{3PV}}{{Mass\;of\;gas}}} = \sqrt {\frac{{3RT}}{M}} \)
\([\because \rho = \frac{M}{V}]\)
⇒ vrms ∝ T
Where, R = universal gas constant, M = molar mass, P = pressure due to density,ρ = density.
Calculation:
Given that, T = 27°C = 27+273 = 300 K, Vrms = 1930 m/sec
\(V_{rms}= \sqrt {\frac{{3PV}}{{Mass\;of\;gas}}} = \sqrt {\frac{{3RT}}{M}} \)
\(1930 = \sqrt {\frac{{3 \times 8.31 \times {{10}^3} \times 300}}{M}} \)
Mass = 2g, Hence the gas is H2.