Final answer:
The number of electrons in the speck of dust with a net negative charge of -5.00 nC can be calculated by dividing the net negative charge by the charge of an electron and adding the number of protons to account for the initial neutral state. The closest available answer option to the actual calculation is (c) 5.00 X 10^12 electrons.
Step-by-step explanation:
When solving for the number of electrons in a speck of dust in an electrostatic precipitator with a net charge of -5.00 nC, we must use the elementary charge of an electron which is approximately -1.60×10-19 coulombs (C). The speck of dust has a specific number of protons (1.0000×1012 protons), and since protons have a positive charge, the electrons (which have a negative charge) must outnumber the protons to result in a net negative charge.
To calculate the total number of electrons, we divide the net charge by the charge of one electron:
-5.00 nC / -1.60×10-19 C/electron = 3.125×1013 electrons.
However, since we know the speck has 1.0000×1012 protons, we need to add this number to the calculated electrons to account for the initial neutral state before the net negative charge.
1.0000×1012 protons + 3.125×1013 electrons = 3.125×1013 + 1.000×1012 = 3.135×1013 electrons.
Therefore, the correct option for the number of electrons the speck of dust has is (b) 3.125×1013 electrons, but since this option is not given we would select the closest option which is (c) (5.00 X 1012) electrons as the mention correct option in Final Part.