A compound is formed by two elements X and Y. The element Y form ccp and atoms of X occupy 1/3 of tetrahedral voids. If the formula of the compund is `X_a Y_b`, then value of `a + b` is

Explanation

To solve the problem, we need to determine the values of \( a \) and \( b \) in the compound formula \( X_a Y_b \) based on the information given about the crystal structure and the occupancy of the tetrahedral voids.

### Step-by-step Solution:

1. **Identify the Structure of Element Y:**
- The problem states that element Y forms a cubic close-packed (CCP) lattice.
- In a CCP lattice, the number of atoms per unit cell is 4.

2. **Determine the Number of Tetrahedral Voids:**
- In a CCP lattice, the number of tetrahedral voids is twice the number of atoms.
- Therefore, for 4 atoms of Y, the number of tetrahedral voids (TV) is:
\[ \text{Number of Tetrahedral Voids} = 2 \times 4 = 8 \]

3. **Calculate the Number of Atoms of X:**
- The problem states that atoms of X occupy \( \frac{1}{3} \) of the tetrahedral voids.
- Therefore, the number of atoms of X is:
\[ \text{Number of X} = \frac{1}{3} \times 8 = \frac{8}{3} \]

4. **Establish the Formula of the Compound:**
- Now we have the number of atoms of X as \( \frac{8}{3} \) and the number of atoms of Y as 4.
- The formula can be written as:
\[ X_{\frac{8}{3}} Y_4 \]

5. **Simplify the Formula:**
- To express the formula in whole numbers, we can multiply both coefficients by 3 to eliminate the fraction:
\[ X_{\frac{8}{3} \times 3} Y_{4 \times 3} \Rightarrow X_8 Y_{12} \]
- This can be further simplified to:
\[ X_2 Y_3 \]

6. **Determine the Values of a and b:**
- From the simplified formula \( X_2 Y_3 \), we can identify:
- \( a = 2 \)
- \( b = 3 \)

7. **Calculate \( a + b \):**
- Finally, we find:
\[ a + b = 2 + 3 = 5 \]

### Final Answer:
The value of \( a + b \) is \( 5 \).

---