The radius of the orbital of electron in the hydrogen atom `0.5 Å`. The speed of the electron is `2 xx 10^(6)m//s`. Then the current in the loop due to the motion of the electron is

Options

A. `1 mA`
B. `1.5 mA`
C. `2.5 mA`
D. `1.5 xx 10^(-2) mA`

Explanation

To find the current in the loop due to the motion of the electron in a hydrogen atom, we can follow these steps:

### Step 1: Understand the relationship between current, charge, and time
The current (I) due to the motion of an electron can be defined as the charge (Q) passing through a point in a circuit per unit time (t). The formula for current is:
\[ I = \frac{Q}{t} \]

### Step 2: Find the time period of the electron's revolution
The time period (T) for one complete revolution of the electron can be calculated using the formula:
\[ T = \frac{2\pi r}{v} \]
where:
- \( r \) is the radius of the orbit (0.5 Å = \( 0.5 \times 10^{-10} \) m)
- \( v \) is the speed of the electron (\( 2 \times 10^6 \) m/s)

### Step 3: Calculate the time period
Substituting the values into the formula:
\[ T = \frac{2\pi (0.5 \times 10^{-10} \, \text{m})}{2 \times 10^6 \, \text{m/s}} \]

Calculating:
\[ T = \frac{3.14 \times (0.5 \times 10^{-10})}{2 \times 10^6} = \frac{1.57 \times 10^{-10}}{2 \times 10^6} = 7.85 \times 10^{-17} \, \text{s} \]

### Step 4: Calculate the charge passing through a point
The charge of an electron (e) is approximately:
\[ e = 1.6 \times 10^{-19} \, \text{C} \]

### Step 5: Calculate the current
Now, substituting the charge and time period into the current formula:
\[ I = \frac{e}{T} = \frac{1.6 \times 10^{-19} \, \text{C}}{7.85 \times 10^{-17} \, \text{s}} \]

Calculating:
\[ I \approx 2.04 \times 10^{-3} \, \text{A} = 2.04 \, \text{mA} \]

### Final Answer
The current in the loop due to the motion of the electron is approximately:
\[ I \approx 2.04 \, \text{mA} \]