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Answer :
To calculate the coulombs of positive charge in 3.9 kg of plutonium, multiply the number of plutonium atoms by 94 (the number of protons per atom) and the charge of a single proton. The result is approximately 1.44 x 10^9 C.
The question asks how many coulombs of positive charge are in 3.9 kg of plutonium (the atomic mass is given as 244 and each plutonium atom has 94 protons). To find the number of atoms in 3.9 kg of plutonium, we use Avogadro's number and the atomic mass. Then, we calculate the total charge by multiplying the number of atoms by the charge of each proton (94 protons per atom) and the charge of a single proton (approximately 1.602 x 10-19 coulombs).
First, we find the number of moles in 3.9 kg of plutonium:
Number of moles = Mass (kg) / Atomic mass (kg/mol)
Since 1 kg = 1000 g, the mass of plutonium is 3900 g, and the atomic mass for calculation purposes is 244 g/mol.
Number of moles = 3900 g / 244 g/mol
≈ 15.98 mol
Next, we use Avogadro's number to find the number of atoms:
Number of atoms = Number of moles X Avogadro's number
Number of atoms ≈ 15.98 mol x 6.022 x 1023 atoms/mol
Number of atoms ≈ 9.62 x 1024 atoms
Finally, the total charge in coulombs is:
Total charge = Number of atoms x Charge per atom
Charge per atom = Number of protons x Charge of one proton
Charge per atom = 94 protons x 1.602 x 10-19 C
Total charge ≈ 9.62 x 1024 atoms x 94 x 1.602 x 10-19 C/proton
Total charge ≈ 1.44 x 109 C
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