A frame made of metalic wire enclosing a surface area A is covered with a soap film. If the area of the frame of metallic wire is reduced by `50%` the energy of the soap film will be changed by:

Options

A. `100%`
B. `75%`
C. `50%`
D. `25%`

Answer

To solve the problem, we need to analyze how the energy of a soap film changes when the area of the frame enclosing it is reduced by 50%.

### Step-by-Step Solution:

1. **Understanding Surface Energy**:
The surface energy (E) of a soap film is given by the formula:
\[ E = \text{Surface Tension} \times \text{Area} \]
For a soap film, which has two surfaces (front and back), the effective area is doubled. Thus, if the area enclosed by the frame is \( A \), the effective area for the soap film is \( 2A \).

2. **Initial Energy Calculation**:
Let the surface tension be \( T \). The initial energy \( E_i \) of the soap film when the area is \( A \) is:
\[ E_i = T \times (2A) = 2TA \]

3. **Reduction of Area**:
If the area of the frame is reduced by 50%, the new area \( A' \) becomes:
\[ A' = \frac{A}{2} \]

4. **New Energy Calculation**:
The new energy \( E_f \) of the soap film with the reduced area is:
\[ E_f = T \times (2A') = T \times \left(2 \times \frac{A}{2}\right) = TA \]

5. **Change in Energy**:
The change in energy \( \Delta E \) can be calculated as:
\[ \Delta E = E_f - E_i = TA - 2TA = -TA \]

6. **Percentage Change in Energy**:
To find the percentage change in energy, we use the formula:
\[ \text{Percentage Change} = \frac{\Delta E}{E_i} \times 100 \]
Substituting the values:
\[ \text{Percentage Change} = \frac{-TA}{2TA} \times 100 = -50\% \]

7. **Conclusion**:
The energy of the soap film decreases by 50%.

### Final Answer:
The energy of the soap film will be changed by **50%** (decrease).