Consider the following statements for an electron moving in nth orbit of hydrogen like species of atomic number Z?
I. Kinetic energy `prop (Z^(2))/(n^(2))`
II. Frequency of revolution `prop (Z^(2))/(n^(3))`
III. Coulombic force of attraction `prop (Z^(3))/(n^(4))`
IV. Momentum `prop (Z)/(n)`
The correct choice is :

Options

A. I, II, IV
B. I, III
C. II, III
D. I, II, III, IV

Explanation

To solve the question regarding the properties of an electron moving in the nth orbit of a hydrogen-like species with atomic number Z, we will analyze each statement provided in the question step by step.

### Step 1: Analyze Kinetic Energy
- The formula for kinetic energy (KE) of an electron is given by:
\[ KE = \frac{1}{2} m v^2 \]
- The velocity \( v \) of the electron in the nth orbit is proportional to \( \frac{Z}{n} \) (where \( Z \) is the atomic number and \( n \) is the principal quantum number).
- Therefore, we can express the kinetic energy as:
\[ KE \propto \left(\frac{Z}{n}\right)^2 = \frac{Z^2}{n^2} \]
- **Conclusion**: Statement I is correct.

### Step 2: Analyze Frequency of Revolution
- The frequency \( f \) of revolution can be derived from the time period \( T \):
\[ f = \frac{1}{T} \]
- The time period \( T \) can be calculated using the circumference of the orbit divided by the velocity:
\[ T \propto \frac{2\pi r}{v} \]
- The radius \( r \) of the nth orbit is given by \( r \propto \frac{n^2}{Z} \) and the velocity \( v \propto \frac{Z}{n} \).
- Thus, we find:
\[ T \propto \frac{n^2}{Z} \cdot \frac{n}{Z} = \frac{n^3}{Z^2} \]
- Therefore, the frequency is:
\[ f \propto \frac{Z^2}{n^3} \]
- **Conclusion**: Statement II is correct.

### Step 3: Analyze Coulombic Force of Attraction
- The Coulombic force \( F \) between the nucleus and the electron is given by:
\[ F \propto \frac{Z^2}{r^2} \]
- Since \( r \propto \frac{n^2}{Z} \), we can substitute this into the force equation:
\[ F \propto \frac{Z^2}{\left(\frac{n^2}{Z}\right)^2} = \frac{Z^2 \cdot Z^2}{n^4} = \frac{Z^4}{n^4} \]
- **Conclusion**: Statement III is incorrect (it should be proportional to \( \frac{Z^2}{n^4} \)).

### Step 4: Analyze Momentum
- The momentum \( p \) of the electron is given by:
\[ p = mv \]
- Since mass \( m \) is constant, we focus on the velocity:
\[ p \propto v \propto \frac{Z}{n} \]
- **Conclusion**: Statement IV is correct.

### Final Conclusion
The correct statements are I, II, and IV. Thus, the correct choice is option A.