Assertion (A): `1 g` of `O_(2)` and `1 g` atom of `O_(3)` have equal number of molecules.
Reason (R ): Mass of 1 mol atom is equal to its gram atomic mass.

Options

A. If both (A) and (R ) are correct and (R ) is the correct explantion for (A)
B. If both (A) and (R ) are correct but (R ) is not the correct explantion for (A)
C. If (A) is correct but (R ) is incorrect.
D. If (A) and (R ) are incorrect.

Explanation

To solve the given question, we need to analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion:**
- The assertion states that `1 g` of `O₂` (oxygen gas) and `1 g atom` of `O₃` (ozone) have an equal number of molecules.
- We need to calculate the number of molecules in both cases.

2. **Calculating the Number of Molecules in `1 g` of `O₂`:**
- The molar mass of `O₂` is approximately `32 g/mol` (16 g/mol for each oxygen atom).
- To find the number of moles in `1 g` of `O₂`:
\[ \text{Number of moles of } O₂ = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{1 g}{32 g/mol} = 0.03125 \text{ moles} \]
- Now, to find the number of molecules:
\[ \text{Number of molecules} = \text{Number of moles} \times N_A = 0.03125 \times 6.022 \times 10^{23} \approx 1.88 \times 10^{22} \text{ molecules} \]

3. **Calculating the Number of Molecules in `1 g atom` of `O₃`:**
- The molar mass of `O₃` is approximately `48 g/mol` (16 g/mol for each oxygen atom, and there are 3 atoms).
- The term `1 g atom` of `O₃` means we are considering `1 mole` of `O₃` since `1 g atom` corresponds to `1 mole` of the substance.
- Therefore, the number of moles in `1 g atom` of `O₃` is `1 mole`.
- The number of molecules in `1 mole` of `O₃` is:
\[ \text{Number of molecules} = 1 \times N_A = 1 \times 6.022 \times 10^{23} \approx 6.022 \times 10^{23} \text{ molecules} \]

4. **Comparing the Number of Molecules:**
- From the calculations, we find that the number of molecules in `1 g` of `O₂` is approximately `1.88 \times 10^{22}`, while in `1 g atom` of `O₃`, it is `6.022 \times 10^{23}`.
- Therefore, the assertion is incorrect because `1 g` of `O₂` does not have the same number of molecules as `1 g atom` of `O₃`.

5. **Understanding the Reason:**
- The reason states that the mass of `1 mole` atom is equal to its gram atomic mass. This statement is true. For example, the gram atomic mass of oxygen is `16 g/mol`, which corresponds to `1 mole` of oxygen atoms.

6. **Conclusion:**
- The assertion is **false** while the reason is **true**. Therefore, the correct answer is that the assertion is incorrect, but the reason is correct.