In the Bohr model of hydrogen atom, the electron is pictured to rotate in a circular orbit of radius `5xx 10^-11 m`, at a speed `2.2 xx 10^6` m/ s. What is the current associated with electron motion?

Explanation

To find the current associated with the electron motion in the Bohr model of the hydrogen atom, we can follow these steps:

### Step 1: Understand the formula for current
The current \( I \) associated with the motion of an electron in a circular orbit can be defined as:
\[ I = \frac{Q}{T} \]
where \( Q \) is the charge of the electron and \( T \) is the time period of one complete revolution.

### Step 2: Define the charge of the electron
The charge of the electron \( Q \) is given as:
\[ Q = e = 1.6 \times 10^{-19} \text{ C} \]

### Step 3: Calculate the time period \( T \)
The time period \( T \) can be expressed in terms of the angular velocity \( \omega \):
\[ T = \frac{2\pi}{\omega} \]
where \( \omega \) (angular velocity) can be calculated using the formula:
\[ \omega = \frac{V}{R} \]
Here, \( V \) is the speed of the electron and \( R \) is the radius of the orbit.

### Step 4: Substitute values for \( V \) and \( R \)
Given:
- \( V = 2.2 \times 10^6 \text{ m/s} \)
- \( R = 5 \times 10^{-11} \text{ m} \)

Now, calculate \( \omega \):
\[ \omega = \frac{2.2 \times 10^6}{5 \times 10^{-11}} = 4.4 \times 10^{17} \text{ rad/s} \]

### Step 5: Calculate the time period \( T \)
Now substitute \( \omega \) into the time period formula:
\[ T = \frac{2\pi}{\omega} = \frac{2 \times \frac{22}{7}}{4.4 \times 10^{17}} \approx \frac{6.28}{4.4 \times 10^{17}} \approx 1.43 \times 10^{-18} \text{ s} \]

### Step 6: Calculate the current \( I \)
Now substitute \( Q \) and \( T \) back into the current formula:
\[ I = \frac{Q}{T} = \frac{1.6 \times 10^{-19}}{1.43 \times 10^{-18}} \approx 0.111 \text{ A} \]

### Step 7: Convert to milliampere
To express the current in milliampere:
\[ I \approx 1.1 \times 10^{-3} \text{ A} = 1.1 \text{ mA} \]

### Final Answer
The current associated with the electron motion is approximately:
\[ I \approx 1.1 \text{ mA} \]

---