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 determining the time required for a body to acquire a total charge of 1 coulomb when it acquires \(10^{10}\) electrons every second, we can follow these steps:

### Step 1: Calculate the charge acquired per second
The charge of a single electron is approximately \(1.6 \times 10^{-19}\) coulombs. Therefore, the total charge acquired by the body in one second when it acquires \(10^{10}\) electrons is calculated as follows:

\[ q = n \cdot e = 10^{10} \cdot (1.6 \times 10^{-19}) \]

Calculating this gives:

\[ q = 1.6 \times 10^{-9} \text{ coulombs} \]

### Step 2: Set up the equation for total charge
We need to find the time \(t\) required to accumulate a total charge \(Q\) of 1 coulomb. The relationship between charge, current, and time is given by:

\[ Q = q \cdot t \]

Where:
- \(Q\) = total charge (1 coulomb)
- \(q\) = charge acquired per second (\(1.6 \times 10^{-9}\) coulombs)
- \(t\) = time in seconds

### Step 3: Rearranging the equation to find time
Rearranging the equation to solve for time \(t\):

\[ t = \frac{Q}{q} \]

Substituting the values we have:

\[ t = \frac{1 \text{ coulomb}}{1.6 \times 10^{-9} \text{ coulombs}} \]

### Step 4: Calculate the time in seconds
Calculating this gives:

\[ t = \frac{1}{1.6 \times 10^{-9}} \approx 0.625 \times 10^{9} \text{ seconds} \]

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

Now, we convert seconds into years:

\[ t \text{ (in years)} = \frac{0.625 \times 10^{9} \text{ seconds}}{31,536,000 \text{ seconds/year}} \]

Calculating this gives:

\[ t \approx 19.8 \text{ years} \approx 20 \text{ years} \]

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

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