Find the difference of air pressure (in `N-m^(-2)`) between the inside and outside of a soap bubble 5 mm in diameter, if the surface tension is `1.6 N-m^(-1)` :-

Options

A. 2560
B. 3720
C. 1208
D. 10132

Answer

To find the difference in air pressure between the inside and outside of a soap bubble, we can use the formula for excess pressure in a soap bubble, which is given by:

\[ \Delta P = \frac{4T}{R} \]

Where:
- \(\Delta P\) is the difference in pressure (in N/m²),
- \(T\) is the surface tension (in N/m),
- \(R\) is the radius of the soap bubble (in meters).

### Step-by-Step Solution:

**Step 1: Identify the given values.**
- Diameter of the soap bubble = 5 mm = 5 x \(10^{-3}\) m
- Surface tension, \(T\) = 1.6 N/m

**Step 2: Calculate the radius of the soap bubble.**
- Radius \(R\) = Diameter / 2 = \( \frac{5 \times 10^{-3}}{2} = 2.5 \times 10^{-3}\) m

**Step 3: Substitute the values into the formula.**
- Now we substitute \(T\) and \(R\) into the formula for excess pressure:

\[ \Delta P = \frac{4 \times 1.6}{2.5 \times 10^{-3}} \]

**Step 4: Perform the multiplication in the numerator.**
- \(4 \times 1.6 = 6.4\)

**Step 5: Divide by the radius.**
- Now, we calculate:

\[ \Delta P = \frac{6.4}{2.5 \times 10^{-3}} = \frac{6.4}{0.0025} \]

**Step 6: Calculate the final value.**
- Performing the division:

\[ \Delta P = 2560 \, \text{N/m}^2 \]

### Final Answer:
The difference of air pressure between the inside and outside of the soap bubble is **2560 N/m²**.