How many coulombs of positive charge are there in 1.03 kg of plutonium, given that its atomic mass is 244 and each plutonium atom has 94 protons?

To determine how many coulombs of positive charge are present in 1.03 kg of plutonium, we'll follow these steps:

1. **Find the number of plutonium atoms in 1.03 kg**:
   - The atomic mass of plutonium (\(Pu\)) is 244 grams per mole.
   - The mass given is 1.03 kg, which is 1030 grams.
   - Using Avogadro's number (\(N_A = 6.022 \times 10^{23}\) atoms/mol), we can find the number of atoms in 1.03 kg of plutonium.

2. **Calculate the total number of protons**:
   - Each plutonium atom has 94 protons.
   - Therefore, the total number of protons is the number of atoms multiplied by 94.

3. **Convert the number of protons to coulombs**:
   - The charge of one proton is \(1.602 \times 10^{-19}\) coulombs.
   - Multiply the total number of protons by this charge to get the total positive charge in coulombs.

Let's calculate it step by step:

### Step 1: Number of plutonium atoms
\[
\text{Number of moles} = \frac{\text{mass}}{\text{atomic mass}} = \frac{1030 \text{ g}}{244 \text{ g/mol}} = 4.2213 \text{ moles}
\]
\[
\text{Number of atoms} = 4.2213 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mole} = 2.542 \times 10^{24} \text{ atoms}
\]

### Step 2: Total number of protons
\[
\text{Total protons} = 2.542 \times 10^{24} \text{ atoms} \times 94 \text{ protons/atom} = 2.390 \times 10^{26} \text{ protons}
\]

### Step 3: Convert protons to coulombs
\[
\text{Total charge} = 2.390 \times 10^{26} \text{ protons} \times 1.602 \times 10^{-19} \text{ C/proton} = 3.828 \times 10^{7} \text{ C}
\]

### Final Answer:
There are approximately \(3.83 \times 10^{7}\) coulombs of positive charge in 1.03 kg of plutonium.

Would you like more details on any part of this solution, or do you have any questions?

Here are some related questions:
1. What is the significance of Avogadro's number in chemical calculations?
2. How does the atomic mass of an element influence the number of atoms in a sample?
3. What role do protons play in determining the charge of an atom?
4. How can you calculate the number of electrons in a sample if you know the number of protons?
5. How would the charge change if the plutonium sample were ionized?

**Tip:** Remember that the charge of an ion is directly proportional to the number of protons in the nucleus, but it can be affected by the loss or gain of electrons.

Discover how to calculate the positive charge in 1.03 kg of plutonium using atomic structure principles and Coulomb's law. Detailed step-by-step solution provided.

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