Respuesta :
Answer : The energy of a photon absorbed by [tex]He^+[/tex] ions is [tex]8.18\times 10^{-18}J[/tex]
Explanation :
The energy of an electron in the nth level is,
[tex]E_n=-\frac{BZ^2}{n^2}[/tex]
where,
[tex]E_n[/tex] = energy of an electron in the nth level
B = constant = [tex]2.18\times 10^{-18}J[/tex]
n = number of energy level
Z = charge on nucleus or number of protons
First we have to calculate the energy of an electron for n = 1 level.
[tex]E_1=-\frac{BZ^2}{1^2}[/tex]
Z = charge on nucleus or number of protons for helium atom = 2
[tex]E_1=-\frac{(2.18\times 10^{-18})\times (2)^2}{1^2}[/tex]
[tex]E_1=-8.72\times 10^{-18}J[/tex]
Now we have to calculate the energy of an electron for n = 4 level.
[tex]E_4=-\frac{BZ^2}{4^2}[/tex]
Z = charge on nucleus or number of protons for helium atom = 2
[tex]E_4=-\frac{(2.18\times 10^{-18})\times (2)^2}{4^2}[/tex]
[tex]E_4=-5.45\times 10^{-19}J[/tex]
Now we have to calculate the energy of a photon that is absorbed by [tex]He^+[/tex] ions.
[tex]E=E_4-E_1[/tex]
[tex]E=(-5.45\times 10^{-19})-(-8.72\times 10^{-18})[/tex]
[tex]E=8.18\times 10^{-18}J[/tex]
Therefore, the energy of a photon absorbed by [tex]He^+[/tex] ions is [tex]8.18\times 10^{-18}J[/tex]
