Check the corretness of the following statement about the Bohr model of hydrogen atom:
(i) The acceleration of the electron in `n = 2` orbit is more than that in `n = 1` orbit.
(ii) The angular momentum of the electron in `n = 2` orbit is more than that in `n = 1` orbit.
(iii) The `KE` of the electron in `n = 2` orbit is more than that in `n = 1` orbit.

Options

A. All the statements are correct.
B. Only (i) and (ii) are correct.
C. Only (ii) and (iii) are correct.
D. Only (iii) and (i) are correct.

Explanation

To check the correctness of the statements about the Bohr model of the hydrogen atom, we will analyze each statement step by step.

### Step 1: Analyze the first statement
**Statement (i): The acceleration of the electron in `n = 2` orbit is more than that in `n = 1` orbit.**

1. **Acceleration Formula**: The acceleration \( a \) of an electron in a circular orbit can be expressed as:
\[ a = \frac{v^2}{r} \]
where \( v \) is the velocity and \( r \) is the radius of the orbit.

2. **Radius in Bohr Model**: The radius of the orbit in the Bohr model is given by:
\[ r_n = n^2 \cdot r_1 \]
where \( r_1 \) is the radius of the first orbit and \( n \) is the principal quantum number.

3. **Velocity Relation**: The velocity of the electron is inversely proportional to \( n \):
\[ v \propto \frac{1}{n} \]

4. **Conclusion for Statement (i)**:
- For \( n = 1 \), the radius \( r_1 \) is smaller than \( r_2 \) (for \( n = 2 \)).
- Since \( r_2 > r_1 \) and \( v_2 < v_1 \), the acceleration in the \( n = 2 \) orbit will be less than in the \( n = 1 \) orbit.
- Therefore, **Statement (i) is incorrect**.

### Step 2: Analyze the second statement
**Statement (ii): The angular momentum of the electron in `n = 2` orbit is more than that in `n = 1` orbit.**

1. **Angular Momentum Formula**: The angular momentum \( L \) of the electron in the Bohr model is given by:
\[ L = n \cdot \frac{h}{2\pi} \]
where \( h \) is Planck's constant.

2. **Conclusion for Statement (ii)**:
- Since \( n = 2 \) gives \( L_2 = 2 \cdot \frac{h}{2\pi} \) and \( n = 1 \) gives \( L_1 = 1 \cdot \frac{h}{2\pi} \), it is clear that \( L_2 > L_1 \).
- Therefore, **Statement (ii) is correct**.

### Step 3: Analyze the third statement
**Statement (iii): The `KE` of the electron in `n = 2` orbit is more than that in `n = 1` orbit.**

1. **Kinetic Energy Formula**: The kinetic energy \( KE \) of the electron is given by:
\[ KE = \frac{1}{2} mv^2 \]
where \( m \) is the mass of the electron.

2. **Velocity Relation**: As previously mentioned, the velocity \( v \) is inversely proportional to \( n \):
\[ v \propto \frac{1}{n} \]
Thus, as \( n \) increases, \( v \) decreases.

3. **Conclusion for Statement (iii)**:
- For \( n = 2 \), the velocity \( v_2 < v_1 \), leading to \( KE_2 < KE_1 \).
- Therefore, **Statement (iii) is incorrect**.

### Final Conclusion:
- The correctness of the statements is as follows:
- Statement (i): Incorrect
- Statement (ii): Correct
- Statement (iii): Incorrect

Thus, only the second statement is correct.