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 proportional to the quantum number n`

• A. R/E
• B. E/v
• C. RE
• D. Vr

Answer 1

Answer: (D)

Vr

Answer 2

Rydberg constant $R = \frac{\varepsilon_{0}n^{2}h^{2}}{\pi mZe^{2}}$

Velocity $v = \frac{Ze^{2}}{2\varepsilon_{0}nh}$ and energy $E = - \frac{mZ^{2}e^{4}}{8\varepsilon_{0}^{2}n^{2}h^{2}}$

Now, it is clear from above expressions R.v ∝ n