Answer :
To calculate the total charge in coulombs due to the protons in 7.00 kg of plutonium, we need to follow these steps:
Determine the number of atoms in 7.00 kg of plutonium:
The atomic mass of plutonium is given as 244 amu (atomic mass units), which means one mole of plutonium has a mass of 244 grams.
First, convert 7.00 kg of plutonium to grams:
[tex]7.00 \text{ kg} \times 1000 \text{ g/kg} = 7000 \text{ g}[/tex]Calculate the number of moles of plutonium using its atomic mass:
[tex]\text{Number of moles} = \frac{7000 \text{ g}}{244 \text{ g/mol}} \approx 28.69 \text{ moles}[/tex]
Calculate the number of plutonium atoms:
- Using Avogadro's number [tex]6.022 \times 10^{23}[/tex] atoms/mol, the number of atoms is:
[tex]\text{Number of atoms} = 28.69 \text{ moles} \times 6.022 \times 10^{23} \frac{\text{atoms}}{\text{mole}} \approx 1.728 \times 10^{25} \text{ atoms}[/tex]
- Using Avogadro's number [tex]6.022 \times 10^{23}[/tex] atoms/mol, the number of atoms is:
Determine the total positive charge from protons:
Each plutonium atom has 94 protons. Therefore, the total number of protons is:
[tex]1.728 \times 10^{25} \text{ atoms} \times 94 \frac{\text{protons}}{\text{atom}} \approx 1.625 \times 10^{27} \text{ protons}[/tex]The charge of one proton is approximately [tex]1.602 \times 10^{-19}[/tex] coulombs. So, the total positive charge is:
[tex]\text{Total charge} = 1.625 \times 10^{27} \text{ protons} \times 1.602 \times 10^{-19} \frac{\text{C}}{\text{proton}} \approx 2.603 \times 10^{8} \text{ C}[/tex]
Therefore, there are approximately [tex]2.603 \times 10^{8}[/tex] coulombs of positive charge present in 7.00 kg of plutonium.
