Final answer:
To find the total coulombs of positive charge in 4.00 kg of plutonium, calculate the number of moles, multiply by Avogadro's number for total atoms, and then multiply by the charge per proton for the total charge. However, the calculated charge does not match any of the given answer choices, suggesting a possible error in the options provided.
Step-by-step explanation:
To calculate the total coulombs of positive charge in 4.00 kg of plutonium, we first need to find the number of plutonium atoms in the sample. Since the atomic mass unit (amu) of plutonium is 244 and one mole of plutonium weighs 244 grams, we can find the number of moles in 4.00 kg (4000 grams) of plutonium:
Number of moles = 4000 g / 244 g/mol = 16.39 mol
Next, using Avogadro's number (6.022 × 1023 atoms/mol), we calculate the number of atoms:
Number of atoms = 16.39 mol × 6.022 × 1023 atoms/mol = 9.86 × 1025 atoms
Since each plutonium atom has 94 protons, and each proton has a charge of +1.6 × 10−19 C:
Total positive charge = 94 protons/atom × 1.6 × 10−19 C/proton × 9.86 × 1025 atoms
Total positive charge = 1.48 × 108 C
However, since none of the answer choices match this value, it's important to double-check the calculations. The discrepancy could be due to an error in the given options or a mistake in the calculations. As a tutor, my objective is to guide you through the correct process, and please ensure that you have the correct answer options available.