Question

(17%) Problem 6: Let's imagine a scenario in which a hypothetical subatomic particle of mass 26 x 10-kg at rest decays into a daughter hypothetical subatomic particle of mass 1.2 x 10-kg while emitting a photon. For simplicity, assume that the speed of the daughter particle is considerably lower than the speed of light. 50% Part (a) Calculate the energy of the photon, in joules. Grade Summary Deductions 049 Potential 10040 ( HOME E sino cos t ano) cotano asino acoso atan acotan sinh cosho tanho cotanho Degrees Radians 7 8 4 5 * 2 0 BACKSPACE 9 6 3 Submissions Attempts remaining: 5 4 per attempt) detailed view - O - END CLEAR Submit Hirt Feedback I give up! Hints: 10 deduction per hint. Hints remainings Feedback 1% deduction per feedback HA 50% Part (b) Find the kinetic energy of the daughter particle, in joules.

Answer 1

a)From conservation of momentum Pi= P, = ymv (1) Using conservation of energy | Mc = c +E (2) From (1) and (2) Ym,cvs Mc-ymcº MMC m; 12- (2.6x10-28 1.2x10-28 CVT (2.16667)- +39 1-) (v - (2.16667)° -1 1+(2.16667) = 0.64878 V=0.649c The Lorentz factor is, 1 1-(0.649) =1.314425918 =1.31

P1 = ym, v = (1.3144)(1.2x10-2)(0.649(3x109)) = 3.07x10-20 kg.m's The kinetic energy is K, = PC = (3.07x10-20 (3x108) =9.21x10-12 J =9.2x10-12 J (b)The energy of the daughter is, Edelgiter = ym.c? = (1.31)(1.2x10-28) (3x108) = 1.4148x10-11 J =1.4x10-11 ]