To solve the problem, we need to determine the number of atoms present in 18 g samples of \( O_2 \), \( N_2 \), \( CH_4 \), and \( H_2O \). We'll do this by calculating the number of moles of each substance and then multiplying by the number of atoms per molecule.
### Step-by-Step Solution:
1. **Calculate the number of moles for each substance:**
- The formula for calculating moles is:
\[
\text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}
\]
2. **For \( O_2 \):**
- Molar mass of \( O_2 = 32 \, \text{g/mol} \)
- Number of moles:
\[
\text{Moles of } O_2 = \frac{18 \, \text{g}}{32 \, \text{g/mol}} = 0.5625 \, \text{mol}
\]
- Number of atoms in \( O_2 \):
\[
\text{Atoms} = 0.5625 \, \text{mol} \times 2 = 1.125 \, N
\]
3. **For \( N_2 \):**
- Molar mass of \( N_2 = 28 \, \text{g/mol} \)
- Number of moles:
\[
\text{Moles of } N_2 = \frac{18 \, \text{g}}{28 \, \text{g/mol}} = 0.6429 \, \text{mol}
\]
- Number of atoms in \( N_2 \):
\[
\text{Atoms} = 0.6429 \, \text{mol} \times 2 = 1.2858 \, N
\]
4. **For \( CH_4 \):**
- Molar mass of \( CH_4 = 16 \, \text{g/mol} \)
- Number of moles:
\[
\text{Moles of } CH_4 = \frac{18 \, \text{g}}{16 \, \text{g/mol}} = 1.125 \, \text{mol}
\]
- Number of atoms in \( CH_4 \):
\[
\text{Atoms} = 1.125 \, \text{mol} \times 5 = 5.625 \, N
\]
5. **For \( H_2O \):**
- Molar mass of \( H_2O = 18 \, \text{g/mol} \)
- Number of moles:
\[
\text{Moles of } H_2O = \frac{18 \, \text{g}}{18 \, \text{g/mol}} = 1 \, \text{mol}
\]
- Number of atoms in \( H_2O \):
\[
\text{Atoms} = 1 \, \text{mol} \times 3 = 3 \, N
\]
6. **Summary of the number of atoms:**
- \( O_2 \): \( 1.125 \, N \)
- \( N_2 \): \( 1.2858 \, N \)
- \( CH_4 \): \( 5.625 \, N \)
- \( H_2O \): \( 3 \, N \)
7. **Decreasing order of number of atoms:**
- \( CH_4 > H_2O > N_2 > O_2 \)
### Final Answer:
The correct decreasing order of the number of atoms present in the samples is:
\[ CH_4 > H_2O > N_2 > O_2 \]
