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 question, we need to analyze both the assertion (A) and the reason (R) provided in the question.

### Step 1: Calculate the moles of \( NH_4^+ \)

Given:
- Mass of \( NH_4^+ = 9 \, \text{g} \)
- Molar mass of \( NH_4^+ \):
- Nitrogen (N) = 14 g/mol
- Hydrogen (H) = 1 g/mol (4 H atoms)

The molar mass of \( NH_4^+ \) is:
\[ \text{Molar mass} = 14 + (4 \times 1) = 18 \, \text{g/mol} \]

Now, we can calculate the number of moles:
\[ \text{Moles of } NH_4^+ = \frac{\text{Mass}}{\text{Molar mass}} = \frac{9 \, \text{g}}{18 \, \text{g/mol}} = 0.5 \, \text{moles} \]

### Step 2: Calculate the number of ions in \( NH_4^+ \)

Since \( NH_4^+ \) is a single ion, the number of ions in 0.5 moles is:
\[ \text{Number of ions} = 0.5 \, \text{moles} \times N_A = 0.5 \times 6.022 \times 10^{23} \approx 3.011 \times 10^{23} \, \text{ions} \]

### Step 3: Compare the number of ions to Avogadro's number

Avogadro's number \( N_A \) is approximately \( 6.022 \times 10^{23} \). Therefore, the number of ions in 9 grams of \( NH_4^+ \) is:
\[ 0.5 \times N_A \neq N_A \]
This shows that the assertion (A) is false.

### Step 4: Analyze the reason (R)

The reason states that "the number of ions is equal to the number of atoms."

For \( NH_4^+ \):
- 1 ion of \( NH_4^+ \) contains:
- 1 Nitrogen atom
- 4 Hydrogen atoms

Thus, for 0.5 moles of \( NH_4^+ \):
- Number of Nitrogen atoms = 0.5 moles
- Number of Hydrogen atoms = \( 0.5 \times 4 = 2 \) moles

The total number of atoms from 0.5 moles of \( NH_4^+ \) is:
\[ \text{Total atoms} = 0.5 \, \text{(N)} + 2 \, \text{(H)} = 2.5 \, \text{moles of atoms} \]

This shows that the number of ions is not equal to the number of atoms. Therefore, the reason (R) is also false.

### Conclusion

Both the assertion (A) and the reason (R) are false.

### Final Answer
Both assertion and reason are false.

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