Question

The magnitude of the charge for a single electron or proton is $1.6 \times 10^{-19} \ \mathrm{C}$.

What is the net charge of a particle that has 20 electrons and 22 protons?

A) $+3.2 \times 10^{-19} \ \mathrm{C}$

B) $-3.2 \times 10^{-19} \ \mathrm{C}$

C) $+1.6 \times 10^{-19} \ \mathrm{C}$

D) $-1.6 \times 10^{-19} \ \mathrm{C}$

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Answer

:

The correct option is $\mathbf{A} \ +3.2 \times 10^{-19} \ \mathrm{C}$.

Protons carry a positive charge of $+1.6 \times 10^{-19} \ \mathrm{C}$ each.

Electrons carry a negative charge of $-1.6 \times 10^{-19} \ \mathrm{C}$ each.

To find the net charge of a particle, you sum the total charges of all protons and electrons present.

Given:

  • Number of protons = 22
  • Number of electrons = 20

Calculating the net charge: $$ \text{Net charge} = 22 \times \left(+1.6 \times 10^{-19} \ \mathrm{C}\right) + 20 \times \left(-1.6 \times 10^{-19} \ \mathrm{C}\right) $$

$$ = 22 \times 1.6 \times 10^{-19} \ \mathrm{C} + 20 \times -1.6 \times 10^{-19} \ \mathrm{C} $$

$$ = 35.2 \times 10^{-19} \ \mathrm{C} - 32 \times 10^{-19} \ \mathrm{C} $$

$$ = 3.2 \times 10^{-19} \ \mathrm{C} $$

Therefore, the net charge of the particle is $+3.2 \times 10^{-19} \ \mathrm{C}$, which corresponds to option A.


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