GATE 2020 MT – Question 46
Mg–Sn has eutectics: at 561°C, liquid (36.9 wt.% Sn) → α (14.48 wt.% Sn) + Mg₂Sn; at 203°C, liquid (97.87 wt.% Sn) → β-Sn (almost 100 wt.% Sn) + Mg₂Sn. For Mg–50 wt.% Sn just below 561°C at equilibrium, approximately what wt.% is eutectic constituent? Atomic weights: Sn 118.7, Mg 24.3.
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Correct answer: (C) 62
Explanation
The line compound contains $C_{Mg_2Sn}=100(118.7)/(118.7+2\times24.3)=70.95$ wt.% Sn. Before the upper eutectic, the 50% alloy consists of liquid at 36.9% and primary Mg₂Sn. Lever rule gives remaining liquid fraction $(70.95-50)/(70.95-36.9)=0.615$. This liquid becomes the eutectic constituent, approximately 62 wt.%, C. The total α fraction below the eutectic is a different quantity.