How many coulombs of positive charge are there in 8.70 kg of plutonium, given its atomic mass is 244 and that each plutonium atom has 94 protons?
To find the number of coulombs of positive charge in 8.70 kg of plutonium, we need to use the following steps:
Step 1: Convert the mass of plutonium from kilograms to grams.
1 kg = 1000 g, so 8.70 kg = 8.70 * 1000 g = 8700 g.
Step 2: Calculate the number of plutonium atoms using Avogadro's number.
1 mole of any element contains Avogadro's number (6.022 x 10^23) atoms.
To find the number of moles, we divide the mass of plutonium by its atomic mass.
Number of moles = Mass of plutonium / Atomic mass
Number of moles = 8700 g / 244 g/mol ≈ 35.66 mol
Step 3: Calculate the number of protons in 35.66 moles of plutonium.
Since each plutonium atom has 94 protons, we multiply the number of moles by the number of protons per atom.
Number of protons = Number of moles x Number of protons per atom
Number of protons = 35.66 mol x 94 protons/mol = 3356.04 protons ≈ 3356 (round to the nearest whole number)
Step 4: Calculate the total positive charge in coulombs.
Since each proton carries a charge of +1.602 x 10^-19 coulombs, we multiply the number of protons by this charge.
Total positive charge = Number of protons x Charge per proton
Total positive charge = 3356 x (1.602 x 10^-19 C/proton) ≈ 5.373 x 10^-17 C (in scientific notation)
Therefore, there are approximately 5.373 x 10^-17 coulombs of positive charge in 8.70 kg of plutonium.