Adiabatic velocity!

An adiabatic chamber has frictionless piston of mass $m$ . Mass of remaining chamber including gas is $4m$ . $n$ moles of an ideal monoatomic gas is present inside the chamber at atmospheric temperature and pressure. Piston is at rest in equilibrium and confined to move along the length of the cylinder. A particle of mass m moving horizontally with speed $v$ , strikes elastically with the piston.

The temperature of the gas when the compression of the gas is maximum is of the form $\frac{Amv^2}{75nR}$ .

Find $A$ .