Question

Let $T_g$ and $T_e$ be the kinetic energies of the electron in the ground and the third excited states of a hydrogen atom. According to the Bohr model, the ratio $T_g/T_e$ is

• A. 3
• B. 4
• C. 9
• D. 16

Hint:

In the Bohr model, both total and kinetic energies scale as $1/n^2$.

Answer 1

The Correct Option is D

Step 1: Write the Bohr model expression.
Kinetic energy of electron in a Bohr orbit: $T_n \propto \dfrac{1}{n^2}$.

Step 2: Identify the energy levels.
Ground state: $n=1$ ⇒ $T_g \propto 1$.
Third excited state: $n=4$ ⇒ $T_e \propto \dfrac{1}{16}$.

Step 3: Compute the ratio.
$\dfrac{T_g}{T_e} = \dfrac{1}{1/16} = 16$.

Step 4: Conclusion.
Thus, $T_g/T_e = 16$.