A deuteron of mass $$M$$ moving at speed $$v$$ collides elastically with an alpha-particle of mass $$2M$$, initially at rest. The deuteron is scattered through $$90^\circ$$ from the initial direction of its motion with speed $$V_d$$ while the alpha-particle is scattered with speed $$V_\alpha$$ at an angle $$\theta$$ from the initial direction. Then

A

$$\theta=30^\circ$$

B

$$V_\alpha=v/\sqrt{3}$$

C

$$V_d=v/\sqrt{3}$$

D

a fraction $$2/3$$ of the energy of deuteron is transferred to the alpha-particle