Question

The diagram shows the energy levels for an electron in a certain atom. Which transition shown represents of a photon with the most energy?

• A. II
• B. I
• C. IV
• D. III

Answer 1

The correct option is D

III

$E_n=-\frac{13.6z^2}{n^2}eV$

Or $E_n=-\frac{k}{n^2}eV$

$E_1=-\frac{k}{1}eV,E_2=-\frac{k}{4}eV,E_4=-\frac{k}{16}eV$

Now, $E_2-E_1=-\frac{k}{4}-(-\frac{k}{1})$

$=k-\frac{k}{4}=\frac{3k}{4}$

$E_4-E_2=-\frac{k}{16}-(-\frac{k}{4})$

$=\frac{k}{4}-\frac{k}{16}=\frac{3k}{16}$

Clearly, $(E_2-E_1)>(E_4-E_2)$

So, (d) is the right choice.