A container filled with air under pressure `P_(0)` contains a soap bubble of radius `R` the air pressure has been reduced to half isothermally and the new radius of the bubble becomes `(5R)/(4)` if the surface tension of the soap water solution. Is S, `P_(0)` is found to be `(12nS)/(R)`. Find the value of n.

Explanation

To solve the problem step by step, we will follow the reasoning laid out in the video transcript while providing clear calculations.

### Step 1: Understand the Initial Conditions
We have a soap bubble with an initial radius \( R \) and an initial pressure \( P_0 \). The pressure inside the bubble is given by:
\[ P_i = P_0 + \frac{4S}{R} \]
where \( S \) is the surface tension of the soap solution.
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