Answer:
The temperature of star is 5473.87 K
Explanation:
Given:
Energy difference [tex]\Delta E = 7.5[/tex] eV
The ratio of number of particle [tex]\frac{N_{f} }{N_{i} } = \frac{1}{2 \times 10^{6} }[/tex]
Degeneracy ratio [tex]\frac{g_{f} }{g_{i} } = 4[/tex]
From the formula of boltzmann distribution for population levels,
[tex]\frac{N_{f} }{N_{i} } =\frac{g_{f} }{g_{i} } e^{-\frac{\Delta E}{kT} }[/tex]
Where [tex]k =[/tex] boltzmann constant = [tex]8.62 \times 10^{-5} \frac{eV}{K}[/tex]
[tex]\frac{1}{2 \times 10^{6} } =4 e^{-\frac{7.5 eV}{8.62 \times 10^{-5} T} }[/tex]
[tex]8 \times 10^{6} } = e^{\frac{7.5 eV}{8.62 \times 10^{-5} T} }[/tex]
[tex]\ln(8 \times 10^{6}) = {\frac{7.5 eV}{8.62 \times 10^{-5} T} }[/tex]
[tex]T = {\frac{7.5 eV}{8.62 \times 10^{-5} \ln(8 \times 10^{6})} }[/tex]
[tex]T = 5473.87[/tex] K
Therefore, the temperature of star is 5473.87 K
