Question

The ratio of surface energy term to volume energy term in the nucleation energy equation at critical condition during the solidification process is:
1. -1/2
2. -3/2
3. -1
4. -2/3

Answer 1

Correct Answer - Option 2 : -3/2

Explanation:

Surface energy = γ × 4πr²

Volume energy = ΔG × (4/3)πr³

\(Critical\;radius\;{r^*} = \left( {\frac{{ - 2\gamma }}{{{\rm{\Delta }}G}}} \right)\)

Ratio of surface energy to volume energy -

\(\frac{{\gamma \; \times \;4\pi {r^2}}}{{{\rm{\Delta }}G \;\times\; \frac{4}{3}\pi {r^3}}}\)

\(\Rightarrow \frac{{3\gamma }}{{r{\rm{\Delta }}G}}\)

At critical radius:

\(\frac{{3\gamma {\rm{\Delta }}G}}{{ - 2\gamma {\rm{\Delta }}G}} \Rightarrow - \frac{3}{2}\)