A system consist of N no. of particles N1.Each particle can have only one of the two energies E1 or E1+ε (ε0).If the system is in equllibrium at temp T, the avg NO.of particles with energy E1 is……

Question

A system consist of N no. of particles N>>1.Each particle can have only one of the two energies E1 or E1+ε (ε>0).If the system is in equllibrium at temp T, the avg NO.of particles with energy E1 is……

michele_laino · Answer

hint:
using the $Boltzmann$ factor, we can write the subsequent expression for the requested average number of particles:
$$\Large \begin{gathered}
  Np = \frac{{N{e^{ - {E_1}/kT}}}}{{{e^{ - {E_1}/kT}} + {e^{ - \left( {{E_1} + \varepsilon } \right)/kT}}}} =  \hfill \
   \hfill \
   = N{e^{ - {E_1}/kT}}\frac{1}{{{e^{ - {E_1}/kT}}\left( {1 + {e^{ - \varepsilon /kT}}} \right)}} = ...? \hfill \ 
\end{gathered} $$

michele_laino · Answer

where $p$ is the probability to get the system in the $E_1$ quantum state, namely the quantum state, with energy $E_1$