Which has least number of atoms ?

Options

A. `1gm O`
B. `1gm O_(2)`
C. `1gm O_(3)`
D. `1 gm F_(2)`

Explanation

To determine which option has the least number of atoms, we will calculate the number of atoms in each of the given substances based on their mass. Let's break it down step by step:

### Step 1: Calculate the number of atoms in 1 gram of Oxygen (O)
- **Molar mass of O** = 16 g/mol
- **Avogadro's number (N_A)** = \(6.022 \times 10^{23}\) atoms/mol

Using the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{1 \text{ g}}{16 \text{ g/mol}} = 0.0625 \text{ mol} \]
Now, calculate the number of atoms:
\[ \text{Number of atoms} = 0.0625 \text{ mol} \times 6.022 \times 10^{23} \text{ atoms/mol} = 0.376 \times 10^{23} \text{ atoms} \]

### Step 2: Calculate the number of atoms in 1 gram of O₂
- **Molar mass of O₂** = 32 g/mol

Using the same approach:
\[ \text{Number of moles} = \frac{1 \text{ g}}{32 \text{ g/mol}} = 0.03125 \text{ mol} \]
Now, calculate the number of atoms:
\[ \text{Number of atoms} = 0.03125 \text{ mol} \times 6.022 \times 10^{23} \text{ atoms/mol} = 0.376 \times 10^{23} \text{ atoms} \]

### Step 3: Calculate the number of atoms in 1 gram of O₃
- **Molar mass of O₃** = 48 g/mol

Using the same approach:
\[ \text{Number of moles} = \frac{1 \text{ g}}{48 \text{ g/mol}} = 0.02083 \text{ mol} \]
Now, calculate the number of atoms:
\[ \text{Number of atoms} = 0.02083 \text{ mol} \times 6.022 \times 10^{23} \text{ atoms/mol} = 0.375 \times 10^{23} \text{ atoms} \]

### Step 4: Calculate the number of atoms in 1 gram of F₂
- **Molar mass of F₂** = 38 g/mol

Using the same approach:
\[ \text{Number of moles} = \frac{1 \text{ g}}{38 \text{ g/mol}} = 0.02632 \text{ mol} \]
Now, calculate the number of atoms:
\[ \text{Number of atoms} = 0.02632 \text{ mol} \times 6.022 \times 10^{23} \text{ atoms/mol} = 0.316 \times 10^{23} \text{ atoms} \]

### Summary of Results:
1. 1 gram of O: \(0.376 \times 10^{23}\) atoms
2. 1 gram of O₂: \(0.376 \times 10^{23}\) atoms
3. 1 gram of O₃: \(0.375 \times 10^{23}\) atoms
4. 1 gram of F₂: \(0.316 \times 10^{23}\) atoms

### Conclusion:
The substance with the least number of atoms is **1 gram of F₂**, which has \(0.316 \times 10^{23}\) atoms.

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