If `10^(9)` electrons move out of a body to another body every second, then the time required to get a total charge of 1 C on the other body is

Options

A. 250 years
B. 100 years
C. 198 years
D. 150 years

Explanation

To solve the problem, we need to determine how long it will take for a total charge of 1 coulomb to accumulate on a body when `10^9` electrons are transferred every second.

### Step-by-Step Solution:

1. **Determine the charge of one electron:**
The charge of a single electron is approximately \( e = 1.6 \times 10^{-19} \) coulombs.

2. **Calculate the total charge transferred per second:**
If \( 10^9 \) electrons move out of the body every second, the total charge transferred in one second can be calculated as:
\[ Q_{\text{per second}} = (10^9 \text{ electrons}) \times (1.6 \times 10^{-19} \text{ C/electron}) = 1.6 \times 10^{-10} \text{ C} \]

3. **Set up the equation for total charge:**
We want to find the time \( t \) required to accumulate a total charge of 1 coulomb. The total charge can be expressed as:
\[ Q_{\text{total}} = Q_{\text{per second}} \times t \]
Setting \( Q_{\text{total}} = 1 \text{ C} \), we have:
\[ 1 \text{ C} = (1.6 \times 10^{-10} \text{ C}) \times t \]

4. **Solve for time \( t \):**
Rearranging the equation gives:
\[ t = \frac{1 \text{ C}}{1.6 \times 10^{-10} \text{ C}} = \frac{1}{1.6 \times 10^{-10}} \text{ seconds} \]
Calculating this:
\[ t \approx 6.25 \times 10^9 \text{ seconds} \]

5. **Convert seconds to years:**
To convert seconds into years, we use the following conversions:
- 1 minute = 60 seconds
- 1 hour = 60 minutes = 3600 seconds
- 1 day = 24 hours = 86400 seconds
- 1 year = 365 days = 31,536,000 seconds

Now, converting seconds to years:
\[ t \text{ (in years)} = \frac{6.25 \times 10^9 \text{ seconds}}{31,536,000 \text{ seconds/year}} \approx 198 \text{ years} \]

### Final Answer:
The time required to accumulate a total charge of 1 coulomb on the other body is approximately **198 years**.

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