Question

Which of the following electron transitions between two energy states () in the hydrogen atom corresponds to the emission of a photon with the longest wavelength?explain why pleasee

8 ? 5
2 ? 5
5 ? 8
5 ? 2

Answer 1

emission of photon is of maximum wavelength when electron transition is from n = 8 to n = 5

Step-by-step 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

`E = -13.6 ((z^2)/(n^2))`

now if z = 1 for hydrogen

then Energy of electron for n = 2

`E_2 = -13.6((1^2)/(2^2))`

`E_2 = -3.4 eV`

Energy of electron for n = 5

`E_5 = -13.6((1^2)/(5^2))`

`E_5 = -0.544 eV`

Energy of electron for n = 8

`E_8 = -13.6((1^2)/(8^2))`

`E_8 = -0.2125 eV`

Now for least energy difference we can say

`\Delta E = E_5 - E_8`

`\Delta E = (-0.2125) - (-0.544) = 0.3315 eV`

So emission of photon is of maximum wavelength when electron transition is from n = 8 to n = 5