what happens to the kinetic energy of a particle when heat energy equivalent to latent heat of fusion is supplied to a solid at its m.pt.
Let suppose you have a bullet that moves and has a kinetic energy and suddenly somehow you heat it until it melts down (you supply enough heat to change the bullet state from solid to liquid). The bullet will split into smaller liquid drops, each having a particular kinetic energy.
The question is: will the sum of all the kinetic energies of the smaller liquid drops be equal to the initial kinetic energy of the solid bullet or not? Will the total kinetic energy stay the same (conserve itself) before and after melting?
The answer is NO. A part of the kinetic energy will be lost.
To demonstrate this let us look into this problem the opposite way. You have a bunch of small drops each having a certain kinetic energy that collides and merge into a single larger drop. Because this is a non-elastic collision (the initial particles merge together) a part of the initial kinetic energy is lost.
The opposite is also true: when melting down and splitting into smaller drops, a part of the initial kinetic energy of the solid will be lost in the process of splitting into smaller drops.