Identify the correct statement(s).
The findings from the Bohr model for H-atom are

Options

A. angular momentum of the electron is expressed as integral multiples of `h/(2pi)`
B. the first Bohr radius is `0.529 Å`
C. the energy of the `n^(th)` level, `E_n` is proportional to `1/(n^2)`
D. the spacing between adjacent levels increases with increase in 'n'

Explanation

To solve the question regarding the findings from the Bohr model for the hydrogen atom, we will analyze each statement one by one and determine their correctness based on the principles of the Bohr model.

### Step-by-Step Solution:

1. **Angular Momentum of the Electron**:
- According to the Bohr model, the angular momentum (L) of the electron in a hydrogen atom is quantized and can be expressed as:
\[ L = mvr = n\frac{h}{2\pi} \]
where \( n \) is a positive integer (1, 2, 3,...), \( h \) is Planck's constant, and \( m \) and \( v \) are the mass and velocity of the electron, respectively.
- **Conclusion**: This statement is **correct**.

2. **First Bohr Radius**:
- The first Bohr radius (r₁) for the hydrogen atom is given as:
\[ r_1 = 0.529 \, \text{Å} \]
This is derived from the formula for the radius of the nth orbit:
\[ r_n = \frac{0.529 \, n^2}{Z} \, \text{Å} \]
For hydrogen (Z = 1) and n = 1, we indeed have:
\[ r_1 = 0.529 \, \text{Å} \]
- **Conclusion**: This statement is **correct**.

3. **Energy of the nth Level**:
- The energy of the electron in the nth orbit is given by:
\[ E_n = -\frac{13.6 Z^2}{n^2} \, \text{eV} \]
For hydrogen (Z = 1), this simplifies to:
\[ E_n = -\frac{13.6}{n^2} \, \text{eV} \]
This indicates that the energy is inversely proportional to the square of n.
- **Conclusion**: This statement is **correct**.

4. **Spacing Between Adjacent Energy Levels**:
- The energy difference between adjacent levels decreases as n increases. For example:
- The energy difference between E1 and E2 is larger than that between E2 and E3.
- As n increases, the energy levels become closer together.
- Therefore, the statement that "the spacing between adjacent levels increases with increase in n" is incorrect.
- **Conclusion**: This statement is **incorrect**.

### Final Conclusions:
- The correct statements from the findings of the Bohr model for the hydrogen atom are:
1. Angular momentum of the electron is expressed as an integral multiple of \( \frac{h}{2\pi} \) (Correct).
2. The first Bohr radius is \( 0.529 \, \text{Å} \) (Correct).
3. The energy of the nth level \( E_n \) is proportional to \( \frac{1}{n^2} \) (Correct).
4. The spacing between adjacent levels increases with increase in n (Incorrect).