According to Bohr's theory of hydrogen atom , for the electron in the nth premissible orbit

Options

A. the linear momentum is propotional to `(1//n)`
B. the radius is propotional to `(n)`
C. the kinetic energy is propotional to `(1//n^(2))`
D. the angular momentum is propotional to `(n)`

Explanation

To solve the question regarding the properties of an electron in the nth permissible orbit of a hydrogen atom according to Bohr's theory, we will analyze each of the given options step by step.

### Step 1: Analyze Linear Momentum
According to Bohr's theory, the linear momentum \( p \) of the electron in the nth orbit is given by:
\[ p \propto \frac{1}{n} \]
This is because the velocity \( v \) of the electron in the nth orbit is inversely proportional to \( n \), and since momentum \( p = mv \) (where \( m \) is the mass of the electron), we conclude that:
\[ p \propto \frac{1}{n} \]
Thus, **Option A is correct**.

### Step 2: Analyze Radius of the Orbit
The radius \( R_n \) of the nth orbit is given by:
\[ R_n = R_0 \frac{n^2}{Z} \]
where \( R_0 \) is the ground state radius and \( Z \) is the atomic number. From this equation, we see that:
\[ R_n \propto n^2 \]
Therefore, **Option B is incorrect**.

### Step 3: Analyze Kinetic Energy
The kinetic energy \( KE \) of the electron in the nth orbit can be expressed as:
\[ KE = \frac{1}{8 \pi \epsilon_0} \frac{Z^2 e^2}{n^2} \]
From this, we can see that:
\[ KE \propto \frac{1}{n^2} \]
Thus, **Option C is correct**.

### Step 4: Analyze Angular Momentum
The angular momentum \( L \) of the electron in the nth orbit is given by:
\[ L = m v_n R_n \]
According to Bohr's quantization condition, angular momentum is also given by:
\[ L = \frac{nh}{2\pi} \]
This shows that:
\[ L \propto n \]
Thus, **Option D is correct**.

### Conclusion
The correct options based on the analysis are:
- **Option A**: Correct
- **Option B**: Incorrect
- **Option C**: Correct
- **Option D**: Correct

### Final Answer
The correct options are A, C, and D.

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