GATE 2024 MT – Question 53
For element A, vacancy-formation enthalpy and entropy per vacancy are 0.5 eV and $3k_B$. Its equilibrium vacancy mole fraction at 500 K is ______ $\times10^{-4}$ (two decimal places). Given: $k_B=8.62\times10^{-5}$ eV atom$^{-1}$ K$^{-1}$.
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Correct answer: 1.7 to 2.0
Explanation
The vacancy fraction is $c_v=\exp(\Delta S_f/k_B)\exp[-\Delta H_f/(k_BT)]$.
Substitute: $c_v=\exp[3-0.5/(8.62\times10^{-5}\times500)]=1.8394\ldots\times10^{-4}$.
The requested coefficient is **1.84**.