What is true about simple cubic type of unit cells?

Options

A. Eight constituents are at different corners of the cube.
B. `Z_(eff) = 1`.
C. Contribution by one corner is `(1)//(8)th` of an atom`.
D. None of the above.

Answer

To determine what is true about simple cubic type of unit cells, we can analyze the properties of this structure step by step.

### Step 1: Understanding the Simple Cubic Unit Cell
A simple cubic unit cell is one of the basic types of crystal structures. In this arrangement, atoms are located only at the corners of the cube.

**Hint:** Remember that a simple cubic unit cell has atoms positioned at specific locations.

### Step 2: Counting the Atoms
In a simple cubic unit cell, there are 8 corners. Each corner atom is shared by 8 adjacent unit cells. Therefore, the contribution of each corner atom to the unit cell is \( \frac{1}{8} \).

**Hint:** Think about how many unit cells share each corner atom.

### Step 3: Calculating the Total Number of Atoms
To find the total number of atoms in a simple cubic unit cell, we multiply the number of corners (8) by the contribution of each corner atom \( \left( \frac{1}{8} \right) \):
\[ \text{Total atoms} = 8 \times \frac{1}{8} = 1 \]
Thus, the effective number of atoms (Z) in a simple cubic unit cell is 1.

**Hint:** Use the formula for total atoms to confirm the effective number.

### Step 4: Evaluating the Options
Now, let's evaluate the options given in the question:
- **Option A:** 8 constituents are at different corners of the cube. (This is misleading; while there are 8 corners, the effective number of atoms is 1.)
- **Option B:** Z effective equals to 1. (This is true, as calculated.)
- **Option C:** Contribution by one corner is one-eighth of an atom. (This is also true, as calculated.)
- **Option D:** None of the above. (This is false since options B and C are true.)

**Hint:** Carefully analyze each option based on the calculations and definitions.

### Conclusion
Based on the analysis:
- **True Statements:**
- Z effective equals to 1 (Option B)
- Contribution by one corner is one-eighth of an atom (Option C)

Thus, the correct statements about simple cubic unit cells are B and C.

**Final Answer:** Options B and C are true about simple cubic type of unit cells.