How many electrons are necessary to produce 10.0 C of negative charge? (e = 1.60 × 10-19 C)

Question

How many electrons are necessary to produce 10.0 C of negative charge? (e = 1.60 × 10-19 C)

BlackTom AI · Accepted Answer

To determine how many electrons are needed to accumulate a total negative charge of 10.0 C, recall that each electron carries a charge of -e where e = 1.60 × 10^-19 C. The count of electrons is given by n = Q / e, using magnitudes for charge calculation: n = 10.0 C / (1.60 × 10^-19 C) = 6.25 × 10^19 electrons. With this in mind, assess each option:

Option 1: 1.60 × 10^9. This value is far too small by about ten orders of magnitude. If you multiplied 1.60 × 10^9 electrons by the elementary charge, you’d only reach roughly 1.60 × 10^9 × 1.60 × 10^-19 C ≈ 2.56 × 10^-10 C, not anywhere near 10 C. This clearly cannot be correct.

Option 2: 6.52 × 10^9. Similar to the first option, this is orders of magnitude too small. The resulting total charge would be on the order of 10^-9 to 10^-8 C, not 10 C, so this is not correct.

Option 3: 6.25 × 10^19. This matches the calculation n = Q / e in magnitude. Multiplying 6.25 × 10^19 electrons by 1.60 × 10^-19 C per electron gives approximately 10 C of charge, which aligns with the target. This is the correct magnitude-based result.

Option 4: 6.15 × 10^23. This is roughly Avogadro-scale and corresponds to a quantity of particles far larger than needed for 10 C. Using 6.15 × 10^23 electrons would yield a total charge around 9.84 C (on the order of a few coulombs) but not the precise 10 C, and the exponent is inconsistent with the direct Q/e calculation for 10 C. This is not the right count.

Option 5: 1.60 × 10^16. This is again far too small; even if you consider 1.60 × 10^16 electrons, the total charge would be about 2.56 × 10^-3 C, which is nowhere near 10 C. This option can be quickly dismissed as incorrect.

In summary, the key idea is to relate total charge to the number of elementary charges via n = Q / e, using the given e = 1.60 × 10^-19 C. The only option that aligns with this calculation to yield 10 C is the one with a 10^19 magnitude, matching 6.25 × 10^19 electrons. The other options fail because their exponents produce charges far from 10 C, either by being many orders of magnitude too small or by using an exponent that corresponds to a much larger particle count than needed.

How many electrons are necessary to produce 10.0 C of negative charge? (e = 1.60 × 10-19 C)单项选择题

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