Calculate number of atoms in each of the following:
I. 0.5 mol of nitrogen
II. 0.2 mole molecules of hydrogen
III. 32 g of sulphur

Options

A. a.`N_(A)//2, 2//5 N_(A), N_(A)//2`
B. b.`N_(A)//2, 1//5 N_(A), N_(A)//2`
C. c.`N_(A)//3, 2//5 N_(A), N_(A)//2`
D. d.`N_(A)/2,N_(A)/5, N_(A)`

Explanation

To calculate the number of atoms in each of the given substances, we will use Avogadro's number, which is \( N_A = 6.022 \times 10^{23} \) atoms/mole.

### Step-by-Step Solution:

**I. Calculate the number of atoms in 0.5 moles of nitrogen (N₂):**

1. **Identify the number of moles:** Given \( 0.5 \) moles of nitrogen.
2. **Determine the number of nitrogen atoms in one mole:** Since nitrogen (N₂) is a diatomic molecule, one mole of nitrogen gas contains \( 2 \) moles of nitrogen atoms.
3. **Calculate the total number of nitrogen atoms:**
\[ \text{Number of atoms} = 0.5 \, \text{moles} \times 2 \, \text{atoms/mole} \times N_A \]
\[ = 0.5 \times 2 \times 6.022 \times 10^{23} = 6.022 \times 10^{23} \text{ atoms} \]

**II. Calculate the number of atoms in 0.2 moles of hydrogen (H₂):**

1. **Identify the number of moles:** Given \( 0.2 \) moles of hydrogen.
2. **Determine the number of hydrogen atoms in one mole:** Since hydrogen (H₂) is also a diatomic molecule, one mole of hydrogen gas contains \( 2 \) moles of hydrogen atoms.
3. **Calculate the total number of hydrogen atoms:**
\[ \text{Number of atoms} = 0.2 \, \text{moles} \times 2 \, \text{atoms/mole} \times N_A \]
\[ = 0.2 \times 2 \times 6.022 \times 10^{23} = 2.4088 \times 10^{23} \text{ atoms} \]

**III. Calculate the number of atoms in 32 g of sulfur (S):**

1. **Identify the mass of sulfur:** Given \( 32 \) g of sulfur.
2. **Determine the molar mass of sulfur:** The molar mass of sulfur (S) is \( 32 \, \text{g/mole} \).
3. **Calculate the number of moles of sulfur:**
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{32 \, \text{g}}{32 \, \text{g/mole}} = 1 \, \text{mole} \]
4. **Calculate the total number of sulfur atoms:**
\[ \text{Number of atoms} = 1 \, \text{mole} \times N_A = 1 \times 6.022 \times 10^{23} = 6.022 \times 10^{23} \text{ atoms} \]

### Final Results:
- **I.** Number of atoms in \( 0.5 \) moles of nitrogen: \( 6.022 \times 10^{23} \) atoms
- **II.** Number of atoms in \( 0.2 \) moles of hydrogen: \( 2.4088 \times 10^{23} \) atoms
- **III.** Number of atoms in \( 32 \) g of sulfur: \( 6.022 \times 10^{23} \) atoms