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Consider a gas in a cubical container 22 cm on a side. How many states lie within ±0.01% of the momentum magnitude p=1.6×10−23  kg⋅m/s (a plausible momentum for a nitrogen molecule in a gas at room temperature)?     The number of states that lie within ±0.01% of the momentum magnitude p=1.6×10−23  kg⋅m/s is  ______× 1025

Consider a gas in a cubical container 22 cm on a side. How many states lie within ±0.01% of the momentum magnitude p=1.6×10−23  kg⋅m/s (a plausible momentum for a nitrogen molecule in a gas at room temperature)?     The number of states that lie within ±0.01% of the momentum magnitude p=1.6×10−23  kg⋅m/s is  ______× 1025

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Consider a gas in a cubical container 22 cm on a side. How many states lie within ±0.01% of the momentum magnitude p=1.6×10−23  kg⋅m/s (a plausible momentum for a nitrogen molecule in a gas at room temperature)?  

 

The number of states that lie within ±0.01% of the momentum magnitude p=1.6×10−23  kg⋅m/s is  ______× 1025.

Expert Solution
Step 1

given, 

side of cubical container =22cm

p=1.6×10-23Kg.m/s

according to Maxwell's statistic, 

The number of state in term of momentum is given by, 

                                g(p)dp=Vh34πp2dp                               (1)

where, V = volume 

           p = momentum 

volume of container, V =(side)3

                                      =(22×10-2)3 =0.011m

p=1.6×10-23Kg.m/s

dp=±0.01% of p    =±0.01% of 1.6×10-23    =1.6×10-27×2    =3.2×10-27                           

   

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