Question

In the Bohr model of the hydrogen atom, let $R$, $v$ and $E$ represent the radius of the orbit, the speed of electron and the total energy of the electron respectively. Which of the following quantity is directly proportional to the quantum number n

• A. $\frac{R}{E}$
• B. $\frac{E}{v}$
• C. $RE$
• D. $Rv$

Answer 1

The correct option is D $Rv$

Radius $R\propto \frac{n^2}{Z^2}$
Velocity $v\propto \frac{Z}{n}$
Energy $E\propto -\frac{Z^2}{n^2}$
Since, for hydrogen atom, $Z$ is 1. Therefore, it is clear from above expressions $Rv$ is directly propotional to $n$.