Considering the following five cases of hydrogen electron transitions, which one describes the emission of light with the highest frequency?

Question

Considering the following five cases of hydrogen electron transitions, which one describes the emission of light with the highest frequency?



-n = 1 to n = 2

-n = 3 to n = 1

-n = 3 to n = 2

-n = 1 to n = 3

-n = 5 to n = 3

Answer 1

For a photon, frequency is directly proportional to energy as shown by E = hν

So, the transition that generates the most energy would be the one with the highest frequency.

n = 1 to n = 2 and n= 1 to n = 3 require an input of energy so you can rule them out.

That leaves

n = 3 to n = 1

n = 3 to n = 2

n = 5 to n = 3

You could use ∆E = 2.179x10^-18(1/n_f² - 1/n_i²) but since we have a constant, we can just look at 1/n_f² - 1/n_i²

n = 3 to n = 1 -> 0.888

n = 3 to n = 2 -> 0.139

n = 5 to n = 3 -> 0.071

So the transition that would produce light of the highest frequency would be n = 3 to n = 1