Answer:
emission of photon is of maximum wavelength when electron transition is from n = 8 to n = 5
Explanation:
Longest wavelength for the transition means the energy difference in two levels must me minimum
So here we know that the energy of electron in a given level is
[tex]E = -13.6 (\frac{z^2}{n^2})[/tex]
now if z = 1 for hydrogen
then Energy of electron for n = 2
[tex]E_2 = -13.6(\frac{1^2}{2^2})[/tex]
[tex]E_2 = -3.4 eV[/tex]
Energy of electron for n = 5
[tex]E_5 = -13.6(\frac{1^2}{5^2})[/tex]
[tex]E_5 = -0.544 eV[/tex]
Energy of electron for n = 8
[tex]E_8 = -13.6(\frac{1^2}{8^2})[/tex]
[tex]E_8 = -0.2125 eV[/tex]
Now for least energy difference we can say
[tex]\Delta E = E_5 - E_8[/tex]
[tex]\Delta E = (-0.2125) - (-0.544) = 0.3315 eV[/tex]
So emission of photon is of maximum wavelength when electron transition is from n = 8 to n = 5
