What should be the diameter of a soap bubble in order that the excess pressure inside it is `20 Nm^(-1)`. Surface tension `= 25 xx 10^(-3) Nm^(-1)`

Explanation

To find the diameter of a soap bubble given the excess pressure and surface tension, we can follow these steps:

### Step 1: Understand the formula for excess pressure in a soap bubble
The excess pressure (\( \Delta P \)) inside a soap bubble is given by the formula:
\[ \Delta P = \frac{4 \sigma}{R} \]
where \( \sigma \) is the surface tension and \( R \) is the radius of the bubble.

### Step 2: Rearrange the formula to find the radius
We can rearrange the formula to solve for the radius \( R \):
\[ R = \frac{4 \sigma}{\Delta P} \]

### Step 3: Substitute the known values
Given:
- Excess pressure \( \Delta P = 20 \, \text{Nm}^{-2} \)
- Surface tension \( \sigma = 25 \times 10^{-3} \, \text{Nm}^{-1} \)

Substituting these values into the equation for \( R \):
\[ R = \frac{4 \times (25 \times 10^{-3})}{20} \]

### Step 4: Calculate the radius
Now, calculate \( R \):
\[ R = \frac{100 \times 10^{-3}}{20} = 5 \times 10^{-3} \, \text{m} \]

### Step 5: Find the diameter
The diameter \( D \) of the soap bubble is twice the radius:
\[ D = 2R = 2 \times (5 \times 10^{-3}) = 10 \times 10^{-3} \, \text{m} \]
This can also be written as:
\[ D = 1.0 \times 10^{-2} \, \text{m} \]

### Final Answer
The diameter of the soap bubble is:
\[ D = 1.0 \times 10^{-2} \, \text{m} \text{ or } 10 \, \text{mm} \]

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