The number of atoms in 0.004 g of magnesium is close to

Options

A. 24
B. `2 xx 10^(20)`
C. `10^(20)`
D. `6.02 xx 10^(23)`

Explanation

To find the number of atoms in 0.004 g of magnesium, we will follow these steps:

### Step 1: Identify the given data
- Given mass of magnesium (Mg) = 0.004 g
- Molar mass of magnesium = 24 g/mol

### Step 2: Calculate the number of moles of magnesium
Using the formula for moles:
\[ \text{Moles} = \frac{\text{Given mass (g)}}{\text{Molar mass (g/mol)}} \]
Substituting the values:
\[ \text{Moles of Mg} = \frac{0.004 \text{ g}}{24 \text{ g/mol}} = 1.6667 \times 10^{-4} \text{ moles} \]

### Step 3: Use Avogadro's number to find the number of atoms
Avogadro's number (N_A) is \(6.022 \times 10^{23}\) atoms/mol. The formula to find the number of atoms is:
\[ \text{Number of atoms} = \text{Moles} \times N_A \]
Substituting the values:
\[ \text{Number of Mg atoms} = 1.6667 \times 10^{-4} \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mol} \]

### Step 4: Perform the calculation
Calculating the number of atoms:
\[ \text{Number of Mg atoms} \approx 1.0 \times 10^{20} \text{ atoms} \]

### Conclusion
Thus, the number of atoms in 0.004 g of magnesium is approximately \(1.0 \times 10^{20}\) atoms.

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