A) \[2{{\left( \frac{6}{\pi } \right)}^{1/2}}\exp (-6)\]
B) \[{{\left( \frac{6}{\pi } \right)}^{1/2}}\exp (-6)\]
C) \[2{{\left( \frac{3}{\pi } \right)}^{1/2}}\exp (-3)\]
D) \[{{\left( \frac{3}{\pi } \right)}^{1/2}}\exp (-3)\]
Correct Answer: C
Solution :
[c] The average kinetic (or thermal energy) \[\overset{-}{\mathop{\varepsilon }}\,=\frac{3}{2}kT\] The fraction of molecules having energies greater than \[\varepsilon \]is given by: \[\frac{N(\varepsilon )}{{{N}_{A}}}=2{{\left( \frac{\varepsilon }{\pi kT} \right)}^{\frac{1}{4}}}\exp (-\varepsilon /kT)\] ?.(i) Now, \[=2\overset{-}{\mathop{\varepsilon }}\,=2\left( \frac{3}{2}kT \right)=3kT.\] Substituting this in equation (i), we have \[\left( \frac{N(\varepsilon )}{{{N}_{A}}} \right)=2{{\left( \frac{3kT}{\pi kT} \right)}^{\frac{1}{2}}}\exp (-3\,kT/kT)\] \[=2{{\left( \frac{3}{\pi } \right)}^{\frac{1}{2}}}\exp (-3)\]
You need to login to perform this action.
You will be redirected in
3 sec
