Question

Sol. [Key Concept: Volume conservation gives $R = 2r$; energy released $= U_{i} - U_{f} = 16\pi\ r^{2}S$.]

Volume conservation

(8) $\left\lbrack \frac{4}{3}\pi r^{3} \right\rbrack = \frac{4}{3}\pi R^{3}$

$$R = 2r $$$U_{i} = (8)\left( 4\pi r^{2} \right)(s);s =$ surface tension

$${U_{i} = 32\pi r^{2}\text{ }s }{U_{f} = \left( 4\pi R^{2} \right)(s) }{U_{f} = 4\pi(2r)^{2}(\text{ }s) = 16\pi r^{2}\text{ }s }$$Energy released $= U_{i} - U_{f}$

Energy released $= 16\pi r^{2}\text{ }s$