A fixed quantity of an ideal monatomic gas is initially in a state with pressure \(P_0\), volume \(V_0\), internal energy \(U_0\), and root-mean-square molecular speed \(v_0\). The gas undergoes a process during which both its pressure and volume are halved to \(\dfrac{1}{2}P_0\) and \(\dfrac{1}{2}V_0\).

Which row in the table correctly identifies the new internal energy \(U_f\) and the new root-mean-square molecular speed \(v_f\) of the gas?

Row	Final Internal Energy \(U_f\)	Final RMS Speed \(v_f\)
A	\(\dfrac{1}{2}U_0\)	\(\dfrac{1}{2}v_0\)
B	\(\dfrac{1}{4}U_0\)	\(\dfrac{1}{4}v_0\)
C	\(\dfrac{1}{4}U_0\)	\(\dfrac{1}{2}v_0\)
D	\(\dfrac{1}{2}U_0\)	\(\dfrac{1}{\sqrt{2}}v_0\)