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