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 of how long it takes for a total charge of 1 coulomb to accumulate on another body when `10^9` electrons are transferred every second, we can follow these steps:

### Step 1: Determine the charge of one electron
The charge of a single electron is approximately:
\[ e = 1.6 \times 10^{-19} \text{ coulombs} \]

### Step 2: Calculate the total charge transferred per second
If `10^9` electrons move out of a body every second, the total charge transferred in one second can be calculated as:
\[ \text{Charge per second} = \text{Number of electrons} \times \text{Charge of one electron} \]
\[ \text{Charge per second} = 10^9 \times 1.6 \times 10^{-19} \text{ C} \]
\[ \text{Charge per second} = 1.6 \times 10^{-10} \text{ C} \]

### Step 3: Calculate the time required to accumulate 1 coulomb
To find the time required to accumulate a total charge of 1 coulomb, we can use the formula:
\[ \text{Time} = \frac{\text{Total Charge}}{\text{Charge per second}} \]
Substituting the values we have:
\[ \text{Time} = \frac{1 \text{ C}}{1.6 \times 10^{-10} \text{ C/s}} \]
\[ \text{Time} = 6.25 \times 10^9 \text{ seconds} \]

### Step 4: Convert seconds into years
To convert seconds into years, we use the conversion factor:
\[ 1 \text{ year} = 365 \times 24 \times 60 \times 60 \text{ seconds} \approx 3.156 \times 10^7 \text{ seconds} \]
Now we can convert the time:
\[ \text{Time in years} = \frac{6.25 \times 10^9 \text{ seconds}}{3.156 \times 10^7 \text{ seconds/year}} \approx 198 \text{ years} \]

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

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