Which of these is true regarding an `alpha` particle with mass 'm' projected towards the nucleus with velocity 'v` ?

Options

A. When the particle stops at distance of closest approach its kinetic energy converts in to electrostatic potential energy
B. number of `alpha` particles that strike the screen is directly proportional to the square of nuclear charge
C. higher the kinetic energy of the `alpha` particle lesser the deflection
D. all the above statement are true

Answer

To solve the question regarding the properties of an alpha particle with mass 'm' projected towards a nucleus with velocity 'v', we can analyze the statements one by one.

### Step-by-Step Solution:

1. **Understanding Kinetic Energy and Potential Energy**:
- When an alpha particle is projected towards a nucleus, it possesses kinetic energy given by the formula:
\[ KE = \frac{1}{2} mv^2 \]
- As the alpha particle approaches the nucleus, it experiences an electrostatic force due to the positive charge of the nucleus. As it gets closer, its speed decreases until it comes to a stop at the closest approach distance.

2. **Conversion of Energy**:
- At the closest approach, the kinetic energy of the alpha particle is completely converted into electrostatic potential energy. The potential energy (PE) between two charged particles can be expressed as:
\[ PE = \frac{k \cdot q_1 \cdot q_2}{r} \]
- Here, \(k\) is Coulomb's constant, \(q_1\) and \(q_2\) are the charges of the alpha particle and the nucleus, and \(r\) is the distance of closest approach.

3. **Statement Evaluation**:
- **Option A**: "When the particle stops at a distance of closest approach, its kinetic energy converts to electrostatic potential energy."
- This statement is true as discussed above.

4. **Number of Alpha Particles and Nuclear Charge**:
- The number of alpha particles that strike a target is proportional to the square of the nuclear charge. This is based on the idea that a higher nuclear charge increases the likelihood of interaction with the alpha particles.
- **Option B**: "Number of alpha particles that strike the screen is directly proportional to the square of nuclear charge."
- This statement is also true.

5. **Kinetic Energy and Deflection**:
- According to Rutherford's model, a higher kinetic energy of an alpha particle results in lesser deflection when it interacts with the nucleus. This is because a faster-moving particle has less time to be influenced by the electrostatic force of the nucleus.
- **Option C**: "Higher the kinetic energy of a particle, lesser the deflection."
- This statement is true as well.

6. **Conclusion**:
- All three statements regarding the alpha particle are correct. Therefore, the answer to the question is that all the statements are true.

### Final Answer:
All the statements regarding the alpha particle are true.