If `10^(10)` electrons are acquired by a body every second, the time required for the body to get a total charge of C will be

Options

A. 2h
B. 2 days
C. 2 yr
D. 20 yr

Answer

To solve the problem of how long it takes for a body to acquire a total charge of 1 coulomb when it gains \(10^{10}\) electrons every second, we can follow these steps:

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

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

### Step 3: Calculate the time required to acquire 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:
\[ \text{Time} = \frac{1 \text{ C}}{1.6 \times 10^{-9} \text{ C/s}} \]
\[ \text{Time} = \frac{1}{1.6 \times 10^{-9}} \text{ seconds} \]
\[ \text{Time} = 6.25 \times 10^{8} \text{ seconds} \]

### Step 4: Convert seconds into years
To convert seconds into years, we can 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, we can convert seconds to years:
\[ \text{Time in years} = \frac{6.25 \times 10^{8} \text{ seconds}}{31,536,000 \text{ seconds/year}} \]
Calculating this gives:
\[ \text{Time in years} \approx 19.8 \text{ years} \]

### Final Answer
Thus, the time required for the body to acquire a total charge of 1 coulomb is approximately 20 years.

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