A coin is made up of Al and weighs 0.75 g. It has a square shape and its diagonal measures 17 mm. It is electrically neutral and contains equal amounts of positive and negative charges. The magnitude of these charges is (Atomic mass of Al = 26.98 g)

Options

A. `3.47xx10^(4)C`
B. `3.47xx10^(2)C`
C. `1.67xx10^(20)C`
D. `1.67xx10^(22)C`

Explanation

To solve the problem step by step, we will calculate the magnitude of the charges present in the aluminum coin.

### Step 1: Determine the number of moles of aluminum in the coin.
Given:
- Mass of aluminum (m) = 0.75 g
- Atomic mass of aluminum (M) = 26.98 g/mol

Using the formula for moles:
\[ \text{Number of moles} (n) = \frac{\text{mass}}{\text{molar mass}} = \frac{m}{M} \]
Substituting the values:
\[ n = \frac{0.75 \, \text{g}}{26.98 \, \text{g/mol}} \approx 0.0278 \, \text{mol} \]

### Step 2: Calculate the number of atoms in the aluminum.
Using Avogadro's number (\(N_A = 6.02 \times 10^{23} \, \text{atoms/mol}\)):
\[ \text{Number of atoms} = n \times N_A = 0.0278 \, \text{mol} \times 6.02 \times 10^{23} \, \text{atoms/mol} \approx 1.67 \times 10^{22} \, \text{atoms} \]

### Step 3: Determine the number of protons (and electrons) in the aluminum.
Each aluminum atom has:
- Atomic number of aluminum = 13 (which means it has 13 protons and 13 electrons).

### Step 4: Calculate the total charge due to protons.
The charge of one proton is approximately \(+1.6 \times 10^{-19} \, \text{C}\). Therefore, the total charge due to all protons is:
\[ \text{Total charge} = \text{Number of protons} \times \text{Charge of one proton} \]
\[ \text{Total charge} = 1.67 \times 10^{22} \, \text{atoms} \times 13 \, \text{protons/atom} \times 1.6 \times 10^{-19} \, \text{C} \]
Calculating this gives:
\[ \text{Total charge} = 1.67 \times 10^{22} \times 13 \times 1.6 \times 10^{-19} \approx 3.47 \times 10^{4} \, \text{C} \]

### Step 5: Conclusion
The magnitude of the positive and negative charges in the aluminum coin is:
\[ \text{Magnitude of charge} \approx 3.47 \times 10^{4} \, \text{C} \]