Question

As the electron in Bohr’s orbit of hydrogen atom passes from state $n$ = 2 to, $n=1$, the Kinetic energy (K) and the potential energy (U) changes as

• A. $K$ four fold, $U$ also four fold
• B. $K$ two fold, $V$ also two fold
• C. $K$ four fold, $U$ two fold
• D. $K$ two fold, $U$ four fold

Answer 1

Answer: (A)

KE of an electron in $n$th orbit : $K_n\propto \frac{1}{n^2}$ and
PE of an electron in $n$th orbit : $U_n\propto \frac{1}{n^2}$
$\therefore$ When an electron passes from state $n=2$ to $n=1$
$\frac{K_2}{K_1}=\frac{1^2}{2^2}=\frac{1}{4}$
$K_1=4K_2$
$\frac{U_2}{U_1}=\frac{1^2}{2^2}=\frac{1}{4}$
or $U_1=4U_2$