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

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

$E = -13.6 (\frac{z^2}{n^2})$

now if z = 1 for hydrogen

then Energy of electron for n = 2

$E_2 = -13.6(\frac{1^2}{2^2})$

$E_2 = -3.4 eV$

Energy of electron for n = 5

$E_5 = -13.6(\frac{1^2}{5^2})$

$E_5 = -0.544 eV$

Energy of electron for n = 8

$E_8 = -13.6(\frac{1^2}{8^2})$

$E_8 = -0.2125 eV$

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