To determine which substance contains the same number of atoms as 20 g of calcium, we need to follow these steps:
### Step 1: Calculate the number of moles of calcium
To find the number of moles, we use the formula:
\[
\text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}
\]
For calcium:
- Mass = 20 g
- Molar mass of calcium = 40 g/mol
Calculating the number of moles:
\[
\text{Number of moles of calcium} = \frac{20 \, \text{g}}{40 \, \text{g/mol}} = 0.5 \, \text{moles}
\]
### Step 2: Calculate the number of atoms in calcium
Using Avogadro's number (\(N_A = 6.022 \times 10^{23} \, \text{atoms/mol}\)), we can find the number of atoms:
\[
\text{Number of atoms} = \text{Number of moles} \times N_A
\]
\[
\text{Number of atoms in calcium} = 0.5 \, \text{moles} \times 6.022 \times 10^{23} \, \text{atoms/mol} = 0.5 N_A
\]
### Step 3: Analyze the options
Now, we need to check each option to see which one has the same number of atoms (0.5 \(N_A\)).
#### Option 1: 24 g of magnesium
- Molar mass of magnesium = 24 g/mol
\[
\text{Number of moles of magnesium} = \frac{24 \, \text{g}}{24 \, \text{g/mol}} = 1 \, \text{mole}
\]
\[
\text{Number of atoms} = 1 \, \text{mole} \times N_A = N_A \, \text{(not equal to 0.5 } N_A\text{)}
\]
#### Option 2: 8 g of oxygen
- Molar mass of oxygen = 16 g/mol
\[
\text{Number of moles of oxygen} = \frac{8 \, \text{g}}{16 \, \text{g/mol}} = 0.5 \, \text{moles}
\]
\[
\text{Number of atoms} = 0.5 \, \text{moles} \times N_A = 0.5 N_A \, \text{(equal to 0.5 } N_A\text{)}
\]
#### Option 3: 12 g of carbon
- Molar mass of carbon = 12 g/mol
\[
\text{Number of moles of carbon} = \frac{12 \, \text{g}}{12 \, \text{g/mol}} = 1 \, \text{mole}
\]
\[
\text{Number of atoms} = 1 \, \text{mole} \times N_A = N_A \, \text{(not equal to 0.5 } N_A\text{)}
\]
#### Option 4: 16 g of oxygen
- Molar mass of oxygen = 16 g/mol
\[
\text{Number of moles of oxygen} = \frac{16 \, \text{g}}{16 \, \text{g/mol}} = 1 \, \text{mole}
\]
\[
\text{Number of atoms} = 1 \, \text{mole} \times N_A = N_A \, \text{(not equal to 0.5 } N_A\text{)}
\]
### Conclusion
The only option that contains the same number of atoms as 20 g of calcium is **Option 2: 8 g of oxygen**.
