Question

For one mole of hydrogen gas, kinetic energy is 4 x 10${}^8$ $erg$. Then its $RMS$ velocity is:

• A. $4\times {10}^{4}cm/sec$
• B. $2\times {10}^{4}cm/sec$
• C. ${10}^7/4cm/sec$
• D. ${10}^{4}cm/sec$

Answer 1

Answer: (B)

$2\times {10}^{4}cm/sec$

$K.E=\frac{1}{2}m{v}_{rms}^2$

Mass of one mole of Hydrogen$=2g.$

$4\times {10}^{8}c{m}^{2}gse{c}^{-2}=\frac{1}{2}\left(2g\right)\left(v_{rms}^2\right)$

$⟹\sqrt{4\times {10}^{8}c{m}^{2}gse{c}^{-2}}=v_{rms}{v}_{rms}=2\times {10}^{4}cm/sec$