Question

Suppose a speck of dust in an electrostatic precipitator has 1.0700 ✕ 10¹² protons in it and has a net charge of −7.80 nC (a very large charge for a small speck). How many electrons does it have?

____________electrons

Answer 1

The speck of dust in the electrostatic precipitator has approximately 1.0700 x 10¹² electrons.

Step-by-step explanation:

Given that the net charge of the speck of dust is
`\( -7.80 \, \text{nC}\)` and it has protons, which are positively charged, the overall charge neutrality implies the presence of electrons, which are negatively charged. To find the number of electrons, we can use the elementary charge e and the given net charge.

The elementary charge e is approximately
`\(1.602 * 10^(-19) \, \text{C}\)` per electron. The formula to calculate the number of electrons
`(\( n_e \))` is:

`\[ n_e = \frac{\text{Net charge}}{\text{Elementary charge}} \]`

Substituting the given values:

`\[ n_e = \frac{-7.80 * 10^(-9) \, \text{C}}{1.602 * 10^(-19) \, \text{C/electron}} \]`

`\[ n_e \approx 1.0700 * 10^(12) \, \text{electrons} \]`

Therefore, the speck of dust has approximately
`\(1.0700 * 10^(12)\)` electrons.