The electrons in a `H`- atom kept at rest , jumps from the mth shell to the nth shell `(m gt n)`. Suppose instead of emitting electromagnetic wave, the energy released is converted into kinetic energy of the atom. Assuming Bohr's model and conservation of angular momentum are valid. Now , answer the following questions:
What principal is violated of inertia

Options

A. Laws of motion
B. Energy conservation
C. Nothing is violated
D. Cannot be decided

Explanation

To solve the problem, we need to analyze the situation described in the question.

### Step-by-Step Solution:

1. **Understanding the Transition**: In a hydrogen atom, when an electron transitions from a higher energy level (mth shell) to a lower energy level (nth shell), it typically emits energy in the form of electromagnetic radiation. However, in this scenario, it is stated that instead of emitting an electromagnetic wave, the energy released is converted into kinetic energy of the atom.

2. **Energy Consideration**: The energy difference between the two shells can be calculated using the formula for the energy levels in a hydrogen atom:
\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]
The energy released during the transition from the mth shell to the nth shell is:
\[ \Delta E = E_m - E_n = -\frac{13.6 \, \text{eV}}{m^2} + \frac{13.6 \, \text{eV}}{n^2} \]

3. **Kinetic Energy of the Atom**: The energy released (\(\Delta E\)) is assumed to be converted into kinetic energy of the atom. This means that the atom will gain kinetic energy equal to the energy difference calculated above.

4. **Conservation of Momentum**: In the absence of external forces, the momentum of the system must be conserved. When the electron jumps to a lower energy level and the atom gains kinetic energy, there is a change in the momentum of the atom due to the change in the electron's energy state.

5. **Violation of Inertia Principle**: The principle of inertia states that an object at rest will remain at rest unless acted upon by a net external force. In this case, if the atom gains kinetic energy without an external force acting on it, it implies that the system is not conserving momentum correctly. This leads to a violation of the laws of motion, specifically Newton's first law.

### Conclusion:
The principle that is violated in this scenario is the **law of inertia** (or Newton's first law of motion). The atom cannot gain kinetic energy without an external force acting on it, which contradicts the principle of inertia.