The number of waves in `n^("th")` orbit are:

Options

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

Explanation

To determine the number of waves in the nth orbit of an electron, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept**:
- Electrons in an atom move in circular orbits around the nucleus. The number of waves in a given orbit can be calculated using the relationship between the circumference of the orbit and the wavelength of the electron.

2. **Circumference of the Orbit**:
- The circumference \( C \) of the orbit in which the electron is moving is given by the formula:
\[ C = 2\pi r \]
where \( r \) is the radius of the orbit.

3. **Wavelength of the Electron**:
- The wavelength \( \lambda \) of the electron can be expressed using de Broglie's hypothesis:
\[ \lambda = \frac{h}{mv} \]
where \( h \) is Planck's constant, \( m \) is the mass of the electron, and \( v \) is the velocity of the electron.

4. **Number of Waves**:
- The number of waves \( N \) in the nth orbit can be calculated by dividing the circumference of the orbit by the wavelength:
\[ N = \frac{C}{\lambda} = \frac{2\pi r}{\lambda} \]

5. **Substituting Wavelength**:
- Now, substitute the expression for wavelength into the equation:
\[ N = \frac{2\pi r}{\frac{h}{mv}} = \frac{2\pi mvr}{h} \]

6. **Using Bohr's Model**:
- According to Bohr's model, the angular momentum of the electron in the nth orbit is quantized and given by:
\[ mvr = \frac{nh}{2\pi} \]
where \( n \) is the principal quantum number.

7. **Final Calculation**:
- Substitute \( mvr \) from Bohr's model into the equation for \( N \):
\[ N = \frac{2\pi \left(\frac{nh}{2\pi}\right)}{h} = n \]

8. **Conclusion**:
- Therefore, the number of waves in the nth orbit is equal to \( n \).

### Final Answer:
The number of waves in the nth orbit is \( n \).

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