According to Bohr's atomic energy :-
(A) Kinetic energy of electron is ` prop (Z^(2))/(n^(2))`.
(B) The product of velocity (v) of electron and principal quantum number(n), `'vn' prop Z^(2)`.
(C) Frequency of revolution of electron in an orbit is ` prop (Z^(3))/(n^(3))`.
(D) Coulombic force of attraction on the electron is ` prop (Z^(3))/(n^(4))`.
Choose the most appropriate answer from the option given below:

Options

A. (C) only
B. (A) only
C. (A),(C) and (D) only
D. (A) and (D) only

Answer

To solve the problem, we need to analyze each statement based on Bohr's atomic theory and determine which ones are correct.

### Step-by-Step Solution:

1. **Kinetic Energy of Electron (Statement A)**:
- According to Bohr's model, the kinetic energy (KE) of an electron in an orbit is given by the formula:
\[ KE = \frac{13.6 \, Z^2}{n^2} \, \text{eV} \]
- This indicates that the kinetic energy is directly proportional to \(Z^2\) and inversely proportional to \(n^2\).
- **Conclusion**: Statement A is **True**.

2. **Product of Velocity and Principal Quantum Number (Statement B)**:
- The velocity \(v\) of an electron in a given orbit is given by:
\[ v = \frac{2.18 \times 10^6 \, Z}{n} \, \text{m/s} \]
- The product of velocity and principal quantum number \(n\) is:
\[ vn = \left(\frac{2.18 \times 10^6 \, Z}{n}\right) n = 2.18 \times 10^6 \, Z \]
- This shows that \(vn\) is directly proportional to \(Z\) and not \(Z^2\).
- **Conclusion**: Statement B is **False**.

3. **Frequency of Revolution of Electron (Statement C)**:
- The frequency \(f\) of an electron's revolution can be derived from its velocity and radius. The formula for frequency is:
\[ f = \frac{v}{2\pi r} \]
- The radius \(r\) is related to \(n\) and \(Z\) as:
\[ r \propto \frac{n^2}{Z} \]
- Substituting the expression for \(v\) and \(r\) into the frequency formula gives:
\[ f \propto \frac{Z}{n^3} \]
- Therefore, the correct relationship shows that frequency is proportional to \(Z^2/n^3\), not \(Z^3/n^3\).
- **Conclusion**: Statement C is **False**.

4. **Coulombic Force of Attraction (Statement D)**:
- The Coulombic force of attraction \(F\) between the nucleus and the electron can be expressed as:
\[ F \propto \frac{Z \cdot e^2}{r^2} \]
- The radius \(r\) can be substituted with \(n^2/Z\) to give:
\[ F \propto \frac{Z \cdot e^2 \cdot Z^2}{n^4} \propto \frac{Z^3}{n^4} \]
- This indicates that the force is indeed proportional to \(Z^3/n^4\).
- **Conclusion**: Statement D is **True**.

### Final Answer:
The correct statements according to Bohr's atomic theory are A and D. Therefore, the most appropriate answer is **Option D**.