Question

A uranium-238 atom can break up into a thorium-234atom and a particle called an alpha particle, α-4. The numbers indicate the inertias of the atoms and the alpha particle in atomic mass units (1 amu = 1.66 × 10−27 kg). When an uranium atom initially at rest breaks up, the thorium atom is observed to recoil with an x component of velocity of -2.1 × 105 m/s.

How much of the uranium atom's internal energy is released in the breakup?

Express your answer to three significant digits and include the appropriate units.

Answer 1

First find the speed of the α particle using conservation of momentum, then find the KE of the two particles.

v = 2.1*10^5m/s * 234/4 = 1.228*10^7 m/s

(ignoring relativistic effects)

Then

KE = ½ * (234*(2.1*10^5m/s)² + 4*(1.228*10^7m/s)²) * 1.66*10^-27kg

KE = 5.092*10^-13 J = 0.509 pJ = 509 fJ