Answer :
Answer:
Relative population is 2.94 x 10⁻¹⁰.
Explanation:
Let N₁ and N₂ be the number of atoms at ground and first excited state of helium respectively and E₁ and E₂ be the ground and first excited state energy of helium respectively.
The ratio of population of atoms as a function of energy and temperature is known as Boltzmann Equation. The equation is:
[tex]\frac{N_{1} }{N_{2} }[/tex] = [tex]\frac{g_{1}e^{\frac{-E_{1} }{KT} } }{g_{2}e^{\frac{-E_{2} }{KT} }}[/tex]
[tex]\frac{N_{1} }{N_{2} }[/tex] = [tex]\frac{g_{1}e^{\frac{-(E_{1}-E_{2}) }{KT} } }{g_{2}}[/tex]
Here g₁ and g₂ be the degeneracy at two levels, K is Boltzmann constant and T is equilibrium temperature.
Put 1 for g₁, 3 for g₂, -19.82 ev for (E₁ - E₂) and 8.6x10⁵ ev/K for K and 10000 k for T in the above equation.
[tex]\frac{N_{1} }{N_{2} }[/tex] = [tex]\frac{1\times e^{\frac{-(-19.82)}{8.6\times 10^{-5}\times 10000} } }{3}[/tex]
[tex]\frac{N_{1} }{N_{2} }[/tex] = 3.4 x 10⁹
[tex]\frac{N_{2} }{N_{1} }[/tex] = 2.94 x 10⁻¹⁰