A uranium nucleus (239U) moves along the positive x-axis with speed vu = 5.0 x 10 m/s when it decays
into an a-particle (He, helium nucleus) and a thorium nucleus (236Th). If He moves off at an angle of
20.2° above the x-axis with a speed V He = 1.4 x 107 m/s, you will determine what is the recoil velocity,
Vth, of 238Th and the angle below the x-axis. Assume the uranium-thorium-alpha system is isolated with
not external forces acting on it and the masses of are AX 1.673 x 10-27 kg. Please note that in the
abbreviation, 4X, X is the atomic abbreviation, Z the number of protons in the nucleus and A the total
number of nucleons (protons plus neutrons). This is a two-dimensional problem.
(a) Write an expression for the conservation of momentum in the x direction in terms of the masses
(mą mon) the velocities (va, Vin) and angles (@q, Oth) measured from the x-axis.
(b) Repeat (a) for the y-direction assuming up is positive.
(c) Write an expression for tan Oth in terms of the masses, velocities and a.
(d) Write an expression for Vrh in terms of ma, mth, Va, 0, and oth:
(e) Evaluate th and Vth.