If the radius of an orbit is `r` and the velocity of electron in it is `v` , then the frequency of electron in the orbit will be

Options

A. `2 pi r v`
B. `(2 pi)/(v r)`
C. `(v r)/(2 pi)`
D. `(v)/(2 pi r)`

Explanation

To find the frequency of an electron in an orbit with radius \( r \) and velocity \( v \), we can follow these steps:

### Step 1: Calculate the Circumference of the Orbit
The circumference \( C \) of the orbit is given by the formula:
\[ C = 2 \pi r \]

### Step 2: Determine the Time Period of the Electron
The time period \( T \) is the time taken for the electron to complete one full orbit. Since the electron travels the circumference at a constant velocity \( v \), the time period can be calculated as:
\[ T = \frac{C}{v} = \frac{2 \pi r}{v} \]

### Step 3: Calculate the Frequency of the Electron
Frequency \( \nu \) is defined as the reciprocal of the time period:
\[ \nu = \frac{1}{T} \]
Substituting the expression for \( T \) from Step 2:
\[ \nu = \frac{1}{\frac{2 \pi r}{v}} = \frac{v}{2 \pi r} \]

### Conclusion
Thus, the frequency of the electron in the orbit is:
\[ \nu = \frac{v}{2 \pi r} \]