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 \[{{\upsilon }_{rms(molecules)}}=\sqrt{\frac{\gamma RT}{M}}=\sqrt{\frac{1.44\times RT}{M}}\] ?(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) \[\frac{{{\upsilon }_{rms(atomic)}}}{{{\upsilon }_{rms(molecular)}}}=\sqrt{\frac{1.66\times R\times 2R\times 2}{M}}\] Hence, \[{{\upsilon }_{rms(atomic)}}=2.18\,{{\upsilon }_{rms(molecular)}}\] \[\approx 2\,{{\upsilon }_{rms(molecular)}}\]
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