Answer: The correct answer is Option C.
Explanation:
We are given a piston of a pump, which means that there is no loss of the air. and there is a change in pressure and volume but temperature of the system remains constant.
As, the pressure of the system increases, there will be more number of particles. So, the number of collisions per unit area will increase.
\(\text{Number of collisions}\propto \text{Pressure}\)
But in the question, volume gets doubled. So, the pressure will be determined by using Boyle's Law:
\(P\propto \frac{1}{V}\)
\(V_2\rightarrow 2V_1\)
where, \(V_1\text{ and }V_2\) are the initial and final volume respectively.
Putting the change in volume in above equation, we get:
\(P_2=\frac{1}{2V_1}\\\\P_2=\frac{1}{2}P_1\)
where, \(P_1\text{ and }P_2\) are the initial and final pressure respectively.
As, the pressure is reduced to half of the initial pressure. So, the number of collisions per unit area will also be reduced to one-half.
Hence, the correct answer is Option C.
