In the Bohr model, the electron of a hydrogen atom moves in circular orbit of radius `5.3xx10^-11` m with speed of `2.2xx10^6 m//s`. Determine its frequency f and the current l in the orbit.

Explanation

To solve the problem, we need to determine the frequency \( f \) of the electron moving in a circular orbit and the current \( I \) associated with that motion.

### Step 1: Calculate the frequency \( f \)

The frequency \( f \) of an electron moving in a circular orbit can be calculated using the formula:

\[ f = \frac{v}{2 \pi r} \]

where:
- \( v \) is the speed of the electron,
- \( r \) is the radius of the orbit.

Given:
- \( v = 2.2 \times 10^6 \, \text{m/s} \)
- \( r = 5.3 \times 10^{-11} \, \text{m} \)

Substituting the values into the formula:

\[ f = \frac{2.2 \times 10^6}{2 \pi (5.3 \times 10^{-11})} \]

Calculating \( 2 \pi \):

\[ 2 \pi \approx 6.2832 \]

Now substituting this value:

\[ f = \frac{2.2 \times 10^6}{6.2832 \times 5.3 \times 10^{-11}} \]

Calculating the denominator:

\[ 6.2832 \times 5.3 \approx 33.33336 \times 10^{-11} \]

Now substituting back:

\[ f = \frac{2.2 \times 10^6}{33.33336 \times 10^{-11}} \approx 6.6 \times 10^{15} \, \text{Hz} \]

### Step 2: Calculate the current \( I \)

The current \( I \) in the orbit can be calculated using the formula:

\[ I = Q \cdot f \]

where:
- \( Q \) is the charge of the electron, approximately \( 1.6 \times 10^{-19} \, \text{C} \),
- \( f \) is the frequency we just calculated.

Substituting the values:

\[ I = (1.6 \times 10^{-19}) \cdot (6.6 \times 10^{15}) \]

Calculating the current:

\[ I = 1.056 \times 10^{-3} \, \text{A} \]

This can also be expressed in milliamperes (mA):

\[ I \approx 1.06 \, \text{mA} \]

### Final Answers:
- Frequency \( f \approx 6.6 \times 10^{15} \, \text{Hz} \)
- Current \( I \approx 1.06 \, \text{mA} \)