Question

A uranium nucleus (238U) moves along the positive ?-axis with speed ? = 5.0 × 105 m/s when it decays

92 ?

into an ?-particle (4He, helium nucleus) and a thorium nucleus (234Th). If 4He moves off at an angle of 2 902

20.2° above the ?-axis with a speed ??? = 1.4 × 107 m/s, you will determine what is the recoil velocity, ? , of 234Th and the angle below the ?-axis. Assume the uranium-thorium-alpha system is isolated with

?h 90

not external forces acting on it and the masses of are A × 1.673 × 10−27 kg. Please note that in the

abbreviation, AX, X is the atomic abbreviation, Z the number of protons in the nucleus and A the total Z

number of nucleons (protons plus neutrons). This is a two-dimensional problem.

1. (a) Write an expression for the conservation of momentum in the ? direction in terms of the masses (?? ??h) the velocities (??,??h) and angles (??,??h) measured from the ?-axis.

2. (b) Repeat (a) for the ?-direction assuming up is positive.

3. (c) Write an expression for tan ??h in terms of the masses, velocities and ?? .

4. (d) Write an expression for ??h in terms of ??, ??h, ??, ?? and ??h.

5. (e) Evaluate ??h and ??h.

Answer 1

Speed of Uranium , V=5x105 mil. (1) mu 9 ļ oma O- 04----- VOT i Dmth Let Va, Ith be find vel. of d-particle and Thorium from Conservation of momentum in x-deon. muv = ma ve COJ Od +mth VT COS Oth 1-) ) doom Conservaton of momenten in Y-cerin. ma Vq Sinda = minth Sindh - (c) droom esna) minth Con Oth=mov-mava coola - in th th Sindth = mavasinad (11) Dividing een-10) by (n), we get Itanatha Mava Sin ad mov-mava colod (d) Squaring and adding ean-1) and (w), we get n v = mx 8x204 + (move ga Co2 0 ) | Vth = my ore Va sm og]?+ (muV-ma Va cosoa]? | e) Smce, ma=u, mu=238, min=234, Vd = 1.4x107m/s, Ud= 20.2" tandth= 4x14x107x Sin 2002- - 0.291 238x5xlov ustvo I OTH = 16.230] Sonderly, VTth = 2.96420 Smols.