The magnitude of angular momentum, orbit radius and frequency of revolution of elctron in hydrogen atom corresponding to quantum number n are L, r and f respectively. Then accoding to Bohr's theory of hydrogen atom

Options

A. `f r^(2)L` is constant for all orbits
B. `f rL` is constant for all orbits
C. `f^(2)rL` is constant for all orbits
D. `f rL^(2)` is constant for all orbits

Explanation

To solve the problem regarding the angular momentum (L), orbit radius (r), and frequency of revolution (f) of an electron in a hydrogen atom according to Bohr's theory, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Forces**:
According to Bohr's theory, the centripetal force acting on the electron due to its circular motion is provided by the electrostatic force of attraction between the positively charged nucleus (proton) and the negatively charged electron.

\[ F_c = \frac{mv^2}{r} \quad \text{(centripetal force)} \]
\[ F_e = \frac{kq^2}{r^2} \quad \text{(electrostatic force)} \]

Where:
- \( m \) = mass of the electron
- \( v \) = velocity of the electron
- \( r \) = radius of the orbit
- \( k \) = Coulomb's constant
- \( q \) = charge of the electron (and proton)

2. **Setting Forces Equal**:
Since the electron is in a stable orbit, these two forces must be equal:

\[ \frac{mv^2}{r} = \frac{kq^2}{r^2} \]

Rearranging gives us:

\[ mv^2 = \frac{kq^2}{r} \]

3. **Relating Angular Momentum**:
The angular momentum \( L \) of the electron in its orbit is given by:

\[ L = mvr \]

From the previous equation, we can express \( mv \) as:

\[ mv = \frac{kq^2}{vr} \]

Substituting this into the angular momentum equation gives:

\[ L = \frac{kq^2}{v} \cdot r \]

4. **Expressing Velocity in Terms of Frequency**:
The velocity \( v \) can also be expressed in terms of frequency \( f \):

\[ v = 2\pi rf \]

Substituting this into the angular momentum equation:

\[ L = \frac{kq^2}{2\pi rf} \cdot r \]

Simplifying this gives:

\[ L = \frac{kq^2}{2\pi f} \]

5. **Identifying Constants**:
From the derived equations, we can see that the product \( f \cdot r \cdot L \) is constant. This means:

\[ f \cdot r \cdot L = \text{constant} \]

### Conclusion:
According to Bohr's theory of the hydrogen atom, the product of the frequency of revolution (f), the orbit radius (r), and the angular momentum (L) is constant for all orbits.