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Answer :
1 mole of plutonium = 244 gm
3.6 kg of plutonium = 3.6 × 1000 = 3600 gm
Number of moles = 3600 ÷ 244 = 14.754 moles
One moles of plutonium contains protons = [tex]\( 6.023 \times {10}^{23} \times 94 \)[/tex]
Total number of protons in 14.754 moles = [tex]\( 6.023 \times {10}^{23} \times 94 \times 14.754 \)[/tex]
Total number of protons in 14.754 moles = [tex]\(8353.15 \times {10}^{23}\)[/tex]
Total Positive charge = [tex]\(8353.15 \times {10}^{23} \times 1.6 \times {10}^{-19}\)[/tex]
Total positive charge = [tex]\(13365.04 \times {10}^{4}\)[/tex] C
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Final answer:
In 3.60 kg of plutonium, with each atom containing 94 protons, there are approximately 1.34 × 10⁶ coulombs of positive charge.
Explanation:
To determine how many coulombs of positive charge there are in 3.60 kg of plutonium, we need to perform a few calculations. Each plutonium atom has 94 protons, and each proton has a charge of approximately 1.602 × 10-19 coulombs. Using the atomic mass of plutonium, which is 244, we can first find the number of moles in 3.60 kg of plutonium. Then, we can find the number of atoms by multiplying by Avogadro's number (approximately 6.022 × 1023 atoms/mole), and then calculate the total charge in coulombs by multiplying by the charge of a single proton.
The number of moles of plutonium in 3.60 kg:
moles = mass (kg) / molar mass (kg/mol)
moles = 3.60 kg / (244 g/mol × 1 kg / 1000 g)
moles = 3.60 kg / 0.244 kg/mol
moles = 14.7541 mol
The number of atoms:
atoms = moles × Avogadro's number
atoms = 14.7541 mol × 6.022 × 1023 atoms/mol
atoms ≈ 8.88 × 1024 atoms
The total charge in coulombs:
charge = atoms × protons/atom × charge/proton
charge = 8.88 × 1024 atoms × 94 × 1.602 × 10-19 C/proton
charge ≈ 1.34 × 106 C
Therefore, there are approximately 1.34 × 106 coulombs of positive charge in 3.60 kg of plutonium.
