The X-X bond length is 1.5 Å and Y-Y bond length is 1.48 Å.If electronegativity values of X and Y are 3 and 3.5 respectively,then Y-X bond length would be

Options

A. `1.44` Å
B. `0.98` Å
C. `1.75` Å
D. `0.73` Å

Answer

To find the Y-X bond length given the bond lengths of X-X and Y-Y, as well as their electronegativity values, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Data:**
- X-X bond length = 1.5 Å
- Y-Y bond length = 1.48 Å
- Electronegativity of X (E_x) = 3
- Electronegativity of Y (E_y) = 3.5

2. **Calculate Atomic Radii:**
- The radius of atom Y (R_y) can be calculated as:
\[ R_y = \frac{\text{Y-Y bond length}}{2} = \frac{1.48 \, \text{Å}}{2} = 0.74 \, \text{Å} \]
- The radius of atom X (R_x) can be calculated as:
\[ R_x = \frac{\text{X-X bond length}}{2} = \frac{1.5 \, \text{Å}}{2} = 0.75 \, \text{Å} \]

3. **Use the Bond Length Formula:**
- The bond length of Y-X (D_Y-X) can be calculated using the formula:
\[ D_{Y-X} = R_y + R_x - 0.09 \times (E_y - E_x) \]

4. **Substitute the Values:**
- Substitute R_y, R_x, E_y, and E_x into the formula:
\[ D_{Y-X} = 0.74 + 0.75 - 0.09 \times (3.5 - 3) \]
- Calculate the difference in electronegativity:
\[ E_y - E_x = 3.5 - 3 = 0.5 \]
- Now substitute this value back into the formula:
\[ D_{Y-X} = 0.74 + 0.75 - 0.09 \times 0.5 \]
- Calculate \(0.09 \times 0.5\):
\[ 0.09 \times 0.5 = 0.045 \]
- Now, calculate the bond length:
\[ D_{Y-X} = 0.74 + 0.75 - 0.045 = 1.445 \, \text{Å} \]

5. **Final Result:**
- The bond length of Y-X is approximately **1.445 Å**.