A) \[0.5\times {{10}^{3}}J,\,241.5K\]
B) \[0.5\times {{10}^{4}}J,\,2415K\]
C) \[{{10}^{3}}J,\,483K,\]
D) \[{{10}^{4}}J,\,4830K\]
Correct Answer: B
Solution :
[b] Mass \[-{{10}^{-22}}g={{10}^{-25}}kg,\] \[{{\mu }_{rms}}={{10}^{5}}cm\,\,{{s}^{-1}}={{10}^{3}}m{{s}^{-1}}\] Total kinetic energy \[=N\left( \frac{1}{2}m{{u}^{2}} \right)\] \[={{10}^{23}}\left( \frac{1}{2}\times ({{10}^{-25}}kg){{({{10}^{3}}m\,\,{{s}^{-1}})}^{2}} \right)\] \[=0.5\times {{10}^{4}}kg\,\,{{m}^{2}}\,{{s}^{-2}}\] \[=0.5\times {{10}^{4}}J\] Total kinetic energy is also equal to \[\left( \frac{3}{2}NkT \right)\] Thus \[\frac{3}{2}NkT=0.5\times {{10}^{4}}J\] \[T=\frac{2}{3}\times \frac{0.5\times {{10}^{4}}J}{Nk}=\frac{2}{3}\times \frac{(0.5\times {{10}^{4}}J)}{({{10}^{23}})(1.38\times {{10}^{-23}}J\,{{K}^{-1}})}\] \[=2415\,K\]
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