A metal block is experiencing an atmospheric pressure of `1 xx 10^(5)N//m^(2)`, when the same block is placed vacuum chamber, the freactional change in its volume is (the bulk modulus of metal is `1.25 xx 10^(11) N//m^(2)`)

Options

A. `4xx10^(-7)`
B. `2xx10^(-7)`
C. `8xx10^(-7)`
D. `1xx10^(-7)`

Explanation

To solve the problem, we need to find the fractional change in volume of a metal block when it is subjected to a change in pressure. The relevant formula involves the bulk modulus of the material.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Atmospheric pressure, \( P_1 = 1 \times 10^5 \, \text{N/m}^2 \)
- Bulk modulus of the metal, \( B = 1.25 \times 10^{11} \, \text{N/m}^2 \)
- Pressure in a vacuum chamber, \( P_2 = 0 \, \text{N/m}^2 \) (since it is a vacuum)

2. **Calculate the Change in Pressure (\( \Delta P \)):**
\[ \Delta P = P_2 - P_1 = 0 - (1 \times 10^5) = -1 \times 10^5 \, \text{N/m}^2 \]

3. **Use the Formula for Bulk Modulus:**
The bulk modulus \( B \) is defined as:
\[ B = -\frac{\Delta P}{\frac{\Delta V}{V}} \]
Rearranging this gives:
\[ \frac{\Delta V}{V} = -\frac{\Delta P}{B} \]

4. **Substitute the Values into the Formula:**
\[ \frac{\Delta V}{V} = -\frac{-1 \times 10^5}{1.25 \times 10^{11}} \]
\[ \frac{\Delta V}{V} = \frac{1 \times 10^5}{1.25 \times 10^{11}} \]

5. **Calculate the Fractional Change in Volume:**
\[ \frac{\Delta V}{V} = \frac{1}{1.25} \times 10^{-6} = 0.8 \times 10^{-6} = 8 \times 10^{-7} \]

### Final Result:
The fractional change in volume of the metal block when placed in a vacuum chamber is:
\[ \frac{\Delta V}{V} = 8 \times 10^{-7} \]