Question

Consider Bohr's theory for hydrogen atom. The magnitude of angular momentum, orbit radius and frequency of the electron in $n^{\text {th }}$ energy state in a hydrogen atom are $L, r\, \&\, f$ respectively. Find out the value of ' $x$ ', if the product $f r L$ is directly proportional to $n^{x}$ :

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (A)

We use
$f r L=\frac{v}{2 \pi r} \times r \times \frac{n h}{2 \pi}=\frac{n h v}{4 \pi^{2}}$
for Bohr's model we have
$v=\frac{k e^{2}}{n h} \times 2 \pi$
$\Rightarrow f r L=\frac{n h}{4 \pi^{2}} \times \frac{k e^{2}}{n h} \times 2 \pi=\frac{k e^{2}}{2 \pi}$
$\Rightarrow f r L=\frac{k e^{2}}{2 \pi}=\frac{k e^{2} n^{0}}{2 \pi}$
$\Rightarrow x=0$