A monoatomic ideal gas is expanded adiabatically to n times of its initial volume. The ratio of final rate of  collision of molecules with unit area of container wall to the initial rate will be

We know that the rate of collision of molecules with unit area of walls of container is proportional to pressure. ThereforeP1V1γ=P2V2γGiven that V2=nV1∴ P1V1γ=P2nV1γNow    P2P1=V1nV1γ=1nγor       P2P1=n−γFor monoatomic gas, γ=53∴ P2P1=n−5/3