`4/25` coulomb of charge contains electrons.

Options

A. `10^(15)`
B. `10^(18)`
C. `10^(20)`
D. none of these

Explanation

To find out how many electrons are contained in a charge of \( \frac{4}{25} \) coulombs, we can follow these steps:

### Step 1: Identify the charge of one electron
The charge of one electron (\( e \)) is approximately \( 1.6 \times 10^{-19} \) coulombs.

### Step 2: Write the formula for the number of electrons
The total charge (\( Q \)) can be expressed in terms of the number of electrons (\( n \)) as:
\[ Q = n \times e \]
From this, we can rearrange the formula to find \( n \):
\[ n = \frac{Q}{e} \]

### Step 3: Substitute the values into the formula
We know \( Q = \frac{4}{25} \) coulombs and \( e = 1.6 \times 10^{-19} \) coulombs. Substituting these values into the formula gives:
\[ n = \frac{\frac{4}{25}}{1.6 \times 10^{-19}} \]

### Step 4: Simplify the expression
To simplify the calculation:
1. Calculate \( \frac{4}{25} \):
\[ \frac{4}{25} = 0.16 \]
2. Now substitute this value into the equation:
\[ n = \frac{0.16}{1.6 \times 10^{-19}} \]

### Step 5: Perform the division
To divide \( 0.16 \) by \( 1.6 \):
\[ n = \frac{0.16}{1.6} \times 10^{19} = 0.1 \times 10^{19} \]

### Step 6: Convert to scientific notation
Now, convert \( 0.1 \) to scientific notation:
\[ 0.1 = 10^{-1} \]
Thus,
\[ n = 10^{-1} \times 10^{19} = 10^{18} \]

### Conclusion
Therefore, the number of electrons contained in \( \frac{4}{25} \) coulombs of charge is:
\[ n = 10^{18} \]

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