An electron is moving in Bohr's fourth orbit. Its de Broglie wavelength is `lambda`. What is the circumference of the fourth orbit?

Options

A. `(2)/(lambda)`
B. `2 lambda`
C. `4 lambda`
D. `(3)/(lambda)`

Answer

To find the circumference of the fourth orbit for an electron moving in Bohr's model, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Bohr's Model**: According to Bohr's theory, the electron moves in circular orbits around the nucleus, and the circumference of the nth orbit is related to the de Broglie wavelength of the electron.

2. **Formula for Circumference**: The circumference \( C \) of the nth orbit can be expressed as:
\[ C = n \lambda \]
where \( n \) is the principal quantum number (the orbit number) and \( \lambda \) is the de Broglie wavelength.

3. **Identify the Given Values**: In this case, we are given that the electron is in the fourth orbit, so:
\[ n = 4 \]

4. **Substituting the Values**: Now, substituting the value of \( n \) into the circumference formula:
\[ C = 4 \lambda \]

5. **Final Answer**: Therefore, the circumference of the fourth orbit is:
\[ C = 4 \lambda \]

### Conclusion:
The circumference of the fourth orbit is \( 4 \lambda \).