`{:(,"List-I",,"List-II"),("(P)","Mass of one atom of C",(1),12xxN_(A)),("(Q)","Number of atoms in 144 g C",(2),12//N_(A)),("(R)","24 g of magnesium",(3),1//N_(A)),("(S)","1 atomic mass unit",(4),N_(A)):}`

Options

A. P-3, Q-2, R-4, S-1
B. P-4, Q-3, R-1, S-2
C. P-2, Q-1, R-3, S-4
D. P-2, Q-1, R-4, S-3

Answer

To solve the problem of matching List-I with List-II, we will analyze each item in List-I and find the corresponding item in List-II based on the information provided.

### Step-by-Step Solution:

1. **Identify (P): Mass of one atom of C**
- The atomic mass of carbon (C) is 12 g/mol.
- To find the mass of one atom of carbon, we use the formula:
\[ \text{Mass of one atom of C} = \frac{\text{Molar mass of C}}{N_A} \]
- Substituting the values:
\[ \text{Mass of one atom of C} = \frac{12 \text{ g}}{N_A} \]
- This matches with option (1) in List-II: \(12 \text{ x } N_A\).

2. **Identify (Q): Number of atoms in 144 g C**
- We know that 12 g of carbon contains \(N_A\) atoms.
- To find the number of atoms in 144 g of carbon, we can set up a proportion:
\[ \text{Number of atoms in 144 g} = N_A \times \frac{144 \text{ g}}{12 \text{ g}} = 12 N_A \]
- This matches with option (2) in List-II: \(12/N_A\).

3. **Identify (R): 24 g of magnesium**
- The molar mass of magnesium (Mg) is approximately 24 g/mol.
- Therefore, 24 g of magnesium corresponds to \(N_A\) atoms.
- This matches with option (3) in List-II: \(1/N_A\).

4. **Identify (S): 1 atomic mass unit**
- By definition, 1 atomic mass unit (amu) is defined as \(1/N_A\) grams.
- This matches with option (4) in List-II: \(N_A\).

### Final Matching:
- (P) matches with (1)
- (Q) matches with (2)
- (R) matches with (3)
- (S) matches with (4)

### Summary of Matches:
- **(P)** → **(1) 12/N_A**
- **(Q)** → **(2) 12/N_A**
- **(R)** → **(3) 1/N_A**
- **(S)** → **(4) N_A**