A: Number of ions in 9 gram of `NH_(4)^(+)` is equal to Avogadro's number (`N_(A)`).
R: Number of ions is equal to number of atoms.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion
C. If Assertion is true statement but Reason is false
D. If both Assertion and Reason are false statements

Answer

To solve the assertion and reason question regarding the number of ions in 9 grams of \( NH_4^+ \) and the relationship between the number of ions and atoms, we will follow these steps:

### Step-by-Step Solution:

1. **Calculate the Molar Mass of \( NH_4^+ \)**:
- The molar mass of \( NH_4^+ \) is calculated as follows:
- Nitrogen (N) has an atomic mass of approximately 14 g/mol.
- Hydrogen (H) has an atomic mass of approximately 1 g/mol, and there are 4 hydrogen atoms in \( NH_4^+ \).
- Therefore, the molar mass of \( NH_4^+ \) is:
\[ \text{Molar mass of } NH_4^+ = 14 + (4 \times 1) = 14 + 4 = 18 \text{ g/mol} \]

2. **Calculate the Number of Moles of \( NH_4^+ \)**:
- Using the formula for moles:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]
- Given mass = 9 g, thus:
\[ \text{Number of moles of } NH_4^+ = \frac{9 \text{ g}}{18 \text{ g/mol}} = \frac{1}{2} \text{ moles} \]

3. **Calculate the Number of Ions in \( NH_4^+ \)**:
- According to Avogadro's number (\( N_A \)), 1 mole of any substance contains \( 6.022 \times 10^{23} \) entities (molecules or ions).
- Therefore, in \( \frac{1}{2} \) mole of \( NH_4^+ \):
\[ \text{Number of ions} = \frac{1}{2} \times N_A = \frac{6.022 \times 10^{23}}{2} = 3.011 \times 10^{23} \text{ ions} \]

4. **Evaluate the Assertion**:
- The assertion states that the number of ions in 9 grams of \( NH_4^+ \) is equal to Avogadro's number (\( N_A \)).
- We found that the number of ions is \( 3.011 \times 10^{23} \), which is not equal to \( 6.022 \times 10^{23} \).
- Thus, the assertion is **false**.

5. **Evaluate the Reason**:
- The reason states that the number of ions is equal to the number of atoms.
- In \( NH_4^+ \), there are 5 atoms (1 nitrogen and 4 hydrogens).
- Therefore, the number of ions (which is \( N_A/2 \)) does not equal the number of atoms (which is \( 5 \times N_A/2 \)).
- Thus, the reason is also **false**.

6. **Conclusion**:
- Both the assertion and the reason are false. Therefore, the correct option is that both assertion and reason are false.