Question

Which of the transitions in hydrogen atom emits a photon of lowest frequency ($n$ = principal quantum number) ?

• A. $n=2$ to $n=1$
• B. $n=4$ to $n=3$
• C. $n=3$ to $n=1$
• D. $n=3$ to $n=2$

Answer 1

The correct option is B $n=4$ to $n=3$

From diagram
$E_1=-13.6-(-3.4)=-10.2\text{eV}(2\to 1)$
$E_2=-13.6-(-1.51)=-12.09\text{eV}(3\to 1)$
$E_3=-1.51-(-0.85)=-0.66\text{eV}(4\to 3)$
$E_4=-3.4-(-1.51)=-0.89\text{eV}(3\to 2)$

$\therefore E_3$ is least, hence frequency is lowest.