A) remains the same
B) becomes \[2\upsilon \]
C) becomes \[\sqrt{2\upsilon }\]
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 \[\gamma =1.66\] \[{{\upsilon }_{rms\,(atomic)}}=\sqrt{1.66\times R\times 2T}\] \[{{\upsilon }_{rms\,(atomic}}=\frac{\sqrt{1.66\times R\times 2T\times 2}}{M}\] ?(2) From equations (1) and (2) \[\frac{{{\upsilon }_{rms\,(atomic)}}}{{{\upsilon }_{rms\,(molecular)}}}=\frac{\sqrt{1.66\times R\times 2T\times 2}}{M}\] \[\times \sqrt{\frac{M}{1.4\times RT}}\] \[=\sqrt{\frac{1.66\times 4}{1.4}}=2.18\] Hence, \[{{\upsilon }_{rms\,(atomic)}}=2.18\,\] \[\approx 2{{\upsilon }_{rms\,(atomic)}}\]
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