Calculate the number of electrons in a small, electrically neutral silver pin that has a mass of `10.0 g`. Silver has 47 electrins per atom, and its molar mass is `107.87 gmol^(-1)`.

Explanation

To calculate the number of electrons in a small, electrically neutral silver pin with a mass of 10.0 g, we can follow these steps:

### Step 1: Calculate the number of moles of silver
To find the number of moles of silver in the pin, we use the formula:

\[ \text{Number of moles} = \frac{\text{mass of silver}}{\text{molar mass of silver}} \]

Given:
- Mass of silver pin = 10.0 g
- Molar mass of silver = 107.87 g/mol

Substituting the values:

\[ \text{Number of moles} = \frac{10.0 \, \text{g}}{107.87 \, \text{g/mol}} \approx 0.0927 \, \text{mol} \]

### Step 2: Calculate the number of atoms of silver
Using Avogadro's number (\(6.022 \times 10^{23} \, \text{atoms/mol}\)), we can find the number of atoms:

\[ \text{Number of atoms} = \text{Number of moles} \times \text{Avogadro's number} \]

Substituting the values:

\[ \text{Number of atoms} = 0.0927 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} \approx 5.58 \times 10^{22} \, \text{atoms} \]

### Step 3: Calculate the total number of electrons
Since each silver atom has 47 electrons, we can find the total number of electrons by multiplying the number of atoms by the number of electrons per atom:

\[ \text{Total number of electrons} = \text{Number of atoms} \times \text{Number of electrons per atom} \]

Substituting the values:

\[ \text{Total number of electrons} = 5.58 \times 10^{22} \, \text{atoms} \times 47 \, \text{electrons/atom} \approx 2.62 \times 10^{24} \, \text{electrons} \]

### Final Answer
The total number of electrons in the silver pin is approximately \(2.62 \times 10^{24}\) electrons.

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