If a current of 1.5 ampere flows through a metallic wire for 3 hours, then how many electrons would flow through the wire?

Options

A. `2.25xx10^22` electrons
B. `1.13xx10^23` electrons
C. `1.01xx10^23` electrons
D. `4.5xx10^23` electrons

Explanation

To solve the problem of how many electrons flow through a metallic wire when a current of 1.5 amperes flows for 3 hours, we can follow these steps:

### Step 1: Identify the given values
- Current (I) = 1.5 A (amperes)
- Time (t) = 3 hours

### Step 2: Convert time from hours to seconds
Since the standard unit of time in physics is seconds, we need to convert hours to seconds:
\[ t = 3 \text{ hours} \times 60 \text{ minutes/hour} \times 60 \text{ seconds/minute} = 10800 \text{ seconds} \]

### Step 3: Calculate the total charge (Q) using the formula
Using the formula \( Q = I \times t \):
\[ Q = 1.5 \text{ A} \times 10800 \text{ s} = 16200 \text{ C} \text{ (coulombs)} \]

### Step 4: Determine the charge of one electron
The charge of one electron is approximately:
\[ e = 1.602 \times 10^{-19} \text{ C} \]

### Step 5: Calculate the number of electrons (n)
To find the number of electrons, we can use the formula:
\[ n = \frac{Q}{e} \]
Substituting the values:
\[ n = \frac{16200 \text{ C}}{1.602 \times 10^{-19} \text{ C/electron}} \approx 1.01 \times 10^{23} \text{ electrons} \]

### Final Answer
The number of electrons that flow through the wire in 3 hours is approximately:
\[ 1.01 \times 10^{23} \text{ electrons} \]

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