An ideal monatomic gas with pressure $$P$$, volume $$V$$ and temperature $$T$$ is expanded isothermally to a volume $$2V$$ and a final pressure $$P_i$$. If the same gas is expanded adiabatically to a volume $$2V$$, the final pressure is $$P_a$$. The ratio $$\frac{P_a}{P_i}$$ is

A

$$2^{-1/3}$$

B

$$2^{1/3^6}$$

C

$$2^{2/3}$$

D

$$2^{-2/3}$$