Assertion (A) : Packing efficiency in simple cubic unit cell is `52.4%`.
Reason (R) : Density of the unit cell is given by the relation : `d=(a^(3)N_(A))/(ZM)`.

Options

A. Both Assertion (A) and Reason (R) are correct statements, and Reason (R) is the correct explanation of the Assertion (A).
B. Both Assertion (A) and Reason (R) are correct statements, but Reason (R) is not the correct explanation of the Assertion (A).
C. Assertion (A) is correct, but Reason (R) is incorrect statement.
D. Assertion (A) is incorrect, but Reason (R) is correct statement.

Answer

To solve the problem, we need to evaluate the assertion and the reason provided in the question regarding the packing efficiency in a simple cubic unit cell and the formula for density.

### Step-by-Step Solution:

1. **Understanding Packing Efficiency**:
- The packing efficiency of a crystal structure is defined as the fraction of volume in a crystal structure that is occupied by the constituent particles (atoms, ions, or molecules).
- For a simple cubic unit cell, there is one atom at each corner of the cube.

2. **Volume of the Atom**:
- The volume \( V \) of a single spherical atom is given by the formula:
\[ V = \frac{4}{3} \pi r^3 \]
- In a simple cubic unit cell, the radius \( r \) of the atom is related to the edge length \( a \) of the cube by the equation:
\[ 2r = a \quad \Rightarrow \quad r = \frac{a}{2} \]

3. **Calculating Volume of the Atom in the Unit Cell**:
- Substituting \( r = \frac{a}{2} \) into the volume formula:
\[ V = \frac{4}{3} \pi \left(\frac{a}{2}\right)^3 = \frac{4}{3} \pi \frac{a^3}{8} = \frac{4 \pi a^3}{24} = \frac{\pi a^3}{6} \]

4. **Volume of the Unit Cell**:
- The volume \( V_{cell} \) of the cubic unit cell is:
\[ V_{cell} = a^3 \]

5. **Calculating Packing Efficiency**:
- The packing efficiency \( PE \) is given by:
\[ PE = \frac{\text{Volume of atoms in unit cell}}{\text{Volume of unit cell}} \times 100 \]
- Since there is one atom per simple cubic unit cell, the packing efficiency becomes:
\[ PE = \frac{\frac{\pi a^3}{6}}{a^3} \times 100 = \frac{\pi}{6} \times 100 \approx 52.4\% \]

6. **Evaluating the Assertion**:
- The assertion states that the packing efficiency in a simple cubic unit cell is 52.4%. This is true based on our calculations.

7. **Understanding the Density Formula**:
- The density \( d \) of a unit cell is given by the formula:
\[ d = \frac{ZM}{a^3 N_A} \]
- Where \( Z \) is the number of atoms per unit cell, \( M \) is the molar mass, \( a \) is the edge length, and \( N_A \) is Avogadro's number.
- The reason provided states that density is given by \( d = \frac{a^3 N_A}{ZM} \), which is incorrect.

8. **Evaluating the Reason**:
- Since the formula for density provided in the reason is incorrect, the reason is false.

### Conclusion:
- The assertion (A) is true, while the reason (R) is false. Therefore, the correct answer is that the assertion is correct, but the reason is incorrect.