Question

How many electrons flow through the wire if a current of 1.5 ampere flow through it for 3 hours?

• A. $1.60 \times 10^{19}$
• B. $1.01 \times 10^{23}$
• C. $1.01 \times 10^{19}$
• D. $1.60 \times 10^{23}$

Hint:

To simplify calculations under pressure, remember that $1\text{ Faraday } (96,500\text{ C})$ is equal to $6.022 \times 10^{23}$ electrons. Since our computed charge ($16,200\text{ C}$) is roughly $\frac{1}{6}$ of a Faraday, our answer must be roughly $\frac{1}{6}$ of Avogadro's number, which points directly to $1.01 \times 10^{23}$.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We are given a steady electric current running through a conducting wire for a specific duration of time. We need to find the total quantity of individual electrons that pass through the cross-section of the wire.

Step 2: Key Formula or Approach:
1. The total electric charge ($Q$) is related to current ($I$) and time ($t$) by: $$Q = I \times t$$ 2. The total charge is also quantized as an integer multiple of the elementary charge of a single electron ($e$): $$Q = n \times e \implies n = \frac{Q}{e}$$ where $e = 1.602 \times 10^{-19}\text{ C}$.

Step 3: Detailed Explanation:
3. Convert the time from hours into standard seconds (s): $$t = 3\text{ hours} = 3 \times 60\text{ minutes} \times 60\text{ seconds} = 10,800\text{ s}$$ 4. Calculate the total charge magnitude $Q$ passing through the wire using the current $I = 1.5\text{ A}$: $$Q = 1.5\text{ A} \times 10,800\text{ s} = 16,200\text{ C}$$ 5. Calculate the number of electrons ($n$) carrying this total charge: $$n = \frac{16,200\text{ C}}{1.602 \times 10^{-19}\text{ C/e}^-}$$ $$n \approx 10,112.36 \times 10^{19}$$ $$n \approx 1.01 \times 10^{23}\text{ electrons}$$

Step 4: Final Answer:
The total number of electrons that flow through the wire is $1.01 \times 10^{23}$, corresponding to option (B).