Number of waves produced by an electron in one complete revolution in `n^(th)` orbit is :

Options

A. n
B. `n^(2)`
C. `(n+1)`
D. `(2n+1)`

Answer

To determine the number of waves produced by an electron in one complete revolution in the \( n^{th} \) orbit, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Orbit**:
An electron in an atom moves in specific orbits or energy levels, denoted by the principal quantum number \( n \). Each orbit corresponds to a certain energy level.

**Hint**: Remember that the principal quantum number \( n \) indicates the energy level of the electron.

2. **Circumference of the Orbit**:
The circumference of the orbit in which the electron is moving can be calculated using the formula for the circumference of a circle:
\[ \text{Circumference} = 2\pi r \]
where \( r \) is the radius of the orbit.

**Hint**: The circumference is the distance the electron travels in one complete revolution.

3. **Wavelength of the Electron**:
When the electron revolves in the orbit, it produces waves. The number of wavelengths that fit into the circumference of the orbit is what we need to calculate. If we denote the wavelength of the electron as \( \lambda \), then the total number of wavelengths \( n \) that fit into the circumference is given by:
\[ n \lambda = 2\pi r \]

**Hint**: Think about how many wavelengths can fit into a given distance.

4. **Relating Wavelength to Principal Quantum Number**:
According to the Bohr model of the atom, the number of wavelengths produced by the electron in one complete revolution in the \( n^{th} \) orbit is equal to \( n \). This means that for each complete revolution, the electron produces \( n \) waves.

**Hint**: The number of waves is directly related to the principal quantum number \( n \).

5. **Conclusion**:
Therefore, the number of waves produced by an electron in one complete revolution in the \( n^{th} \) orbit is simply \( n \).

**Final Answer**: The number of waves produced is \( n \).