Chose the currect on the basis of Bohr's theory

Options

A. Velocity of electron `prop(1)/(n)`
B. frequancy of revolution `prop (Z^(2))/(n^(3))`
C. radius of orbit `prop n^(2)Z`
D. force on electron `prop (Z^(3))/(n^(4))`

Explanation

To solve the question based on Bohr's theory, we will analyze the key concepts and relationships derived from Bohr's model of the atom. Here’s a step-by-step breakdown:

### Step 1: Understand Bohr's Model
Bohr's model describes the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus. The model is based on quantized energy levels.

### Step 2: Key Equations from Bohr's Theory
1. **Velocity of Electron (v)**: According to Bohr's theory, the velocity of an electron in the nth orbit is given by:
\[ v = \frac{2\pi k z e^2}{n h} \]
where:
- \( k \) is Coulomb's constant,
- \( z \) is the atomic number,
- \( e \) is the charge of the electron,
- \( n \) is the principal quantum number,
- \( h \) is Planck's constant.

2. **Radius of Orbit (r)**: The radius of the nth orbit is given by:
\[ r = \frac{0.529 n^2}{z} \]
This shows that the radius is directly proportional to \( n^2 \) and inversely proportional to \( z \).

3. **Time Period (T)**: The time period of the electron in its orbit can be expressed as:
\[ T = \frac{2\pi r}{v} \]
Substituting the expressions for \( r \) and \( v \), we find:
\[ T \propto \frac{n^3}{z^2} \]

4. **Frequency (f)**: The frequency is the reciprocal of the time period:
\[ f = \frac{1}{T} \propto \frac{z^2}{n^3} \]

### Step 3: Analyze the Options
Based on the derived equations, we can analyze the correctness of the given options:

- **Force on Electron**: The force can be expressed in terms of \( z \) and \( n \). If the expression is \( \frac{z^3}{n^4} \), it can be derived from the electrostatic force equation, which is consistent with Bohr's theory.

- **Velocity of Electron**: The velocity is inversely proportional to \( n \), which aligns with the derived expression.

- **Radius of Orbit**: The expression \( n^2 z \) is incorrect since the correct relationship is \( r \propto \frac{n^2}{z} \).

### Conclusion
Based on the analysis:
- The correct options are A (Force on electron), B (Velocity of electron), and D (Frequency).

### Final Answer
The correct options based on Bohr's theory are A, B, and D.

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