A current of 5.0 A flows through an electrical device for 10 seconds. How many electrons flow through this device during this time? (e = 1.60 × 10-19 C)

Question

BlackTom AI · Accepted Answer

We start by identifying what the problem asks: the number of electrons passing through the device given current and time.
First, convert current and time to total charge: Q = I × t. With I = 5 A and t = 10 s, Q = 5 × 10 = 50 coulombs.
Next, relate charge to number of electrons using the elementary charge e = 1.60 × 10^-19 C per electron. The number of electrons N is N = Q / e = 50 / (1.60 × 10^-19).
Compute the division: 50 / 1.60 = 31.25, and 10^(-19) in the denominator moves to 10^19 in the numerator, giving N ≈ 3.125 × 10^20 electrons.
Rounding to two significant figures as typical for these options, N ≈ 3.1 × 10^20.
Now evaluate each option:
Option 1: 20. This is far too small; it would correspond to a charge of about 20 × 1.60 × 10^-19 C, orders of magnitude less than 50 C, so incorrect.
Option 2: 2.0. Even if read as a plain number, it does not incorporate the 10^20 scale and is not close to the calculated value, so incorrect.
Option 3: 3.1 × 10^30. The exponent is off by 10 powers of ten; this would imply an enormous charge far beyond 50 C, so incorrect.
Option 4: 0.20. Like option 2, this lacks the correct magnitude and does not match the calculation of 50 C, so incorrect.
Option 5: 3.1 × 10^20. This matches the computed result N ≈ 3.1 × 10^20 electrons, aligning with Q/e = 50/(1.6×10^-19).
In summary, only the fifth option shows the correct magnitude and aligns with the relationship between current, time, charge, and elementary charge. The other choices either miscalculate the total charge, misplace the exponent, or ignore the electron-counting relation.

A current of 5.0 A flows through an electrical device for 10 seconds. How many electrons flow through this device during this time? (e = 1.60 × 10-19 C) 单项选择题

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