A) \[1:4\]
B) \[1:16\]
C) \[4:1\]
D) \[16:1.\]
Correct Answer: A
Solution :
The root mean square velocity is defined as the square of different velocities possessed by molecules of a gas at a given temperature. \[{{V}_{rms}}=\sqrt{\frac{3kT}{m}}\] \[\Rightarrow \] \[{{V}_{rms}}\propto \frac{1}{\sqrt{m}}\] m = mass of gas molecules \[density=\frac{mass}{volume}\] \[\Rightarrow \] \[{{V}_{rms}}\propto \frac{1}{\sqrt{density}}\] \[\Rightarrow \] \[\frac{{{V}_{rms}}({{O}_{2}})}{{{V}_{rms}}({{H}_{2}})}=\sqrt{\frac{density\,of\,{{H}_{2}}}{density\,of\,{{O}_{2}}}}\] \[=\sqrt{\frac{1}{16}}=\frac{1}{4}\]
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