Question

The magnitude of energy, the magnitude of linear momentuin and orbital radius of an electron in a hydrogen atom corresponding to the quantum number $n$ are $E, P$ and $r$ respectively. Then according to Bohr's theory of hydrogen atom :

• A. $EPr$ is proportional to $\frac{1}{n}$
• B. $P / E$ is proportional to $n$
• C. $Er$ is constant for all orbits
• D. $P$ r is proportional to $n$

Answer 1

Answer: (A), (B), (C), (D)

Energy of electron in $n^{\text {th }}$ orbit is
$E=-\frac{2 \pi^{2} K^{2} Z^{2} e^{4} m_{e}}{n^{2} h^{2}}$
Momentum of electron in $n^{\text {th }}$ orbit is
$P=m V_{n}=\frac{n h}{2 \pi r}$
where $r$ is given as
$r=\frac{n^{2} h^{2}}{2 \pi K Z e^{2} m_{e}}$