A) remains the same
B) becomes 2v
C) becomes \[\sqrt{2v}\]
D) none of these
Correct Answer: B
Solution :
The rms velocity of sound in gas is \[{{\upsilon }_{rms(molecules)}}=\frac{\sqrt{\gamma RT}}{M}=\frac{\sqrt{1.4\times RT}}{M}\] ?.(1) when the oxygen dissociates, its molecular mass becomes atomic mass, so, \[M=\frac{M}{2}\] and \[T=2T\] given and \[\gamma =1.66\] \[{{\upsilon }_{rms(atomic)}}=\frac{\sqrt{1.66\times R\times 2T}}{M/2}\] \[=\frac{\sqrt{1.66\times R\times 2T\times 2}}{M}\] ?..(2) From equations (1) and (2) \[\frac{{{\upsilon }_{rms\,(atomic)}}}{{{\upsilon }_{rms}}_{(molecular)}}=\frac{\sqrt{1.66\times R\times 2T\times 2}}{M}\] \[\times \frac{\sqrt{M}}{1.4\times RT}\] \[=\frac{\sqrt{1.66\times 4}}{1.4}=2.18\] Hence, \[{{\upsilon }_{rms(atomic)}}=2.18{{\upsilon }_{rms(molecular)}}\] \[=2{{\upsilon }_{rms\,(molecular)}}\]
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