Uranium-238 is radioactive. A uranium nucleus (mass 238u, charge 92e) at rest de

Question

Uranium-238 is radioactive. A uranium nucleus (mass 238u, charge 92e) at rest decays by emitting an alpha particle (mass 4u, charge 2e; essentially a helium nucleus), leaving behind a smaller (daughter) nucleus. This process can by modeled in the following way: the original uranium nucleus is basically a 7.4fm radius sphere. Two protons and two neutrons “pinch o” to form the alpha particle, which is initially at rest and immediately adjacent to the remaining nucleons (the daughter). You can assume that at this moment their (center-to-center) separation is 7.4fm. These two positively charged particles will then repel, “emitting” the alpha.
a. What is the mass (in u) and charge (in e) of the daughter nucleus? What is the name of this chemical element?

b. What is the total electrostatic potential energy of the alpha and daughter right after forming?

c. Find the speed of the daughter and the alpha after they have moved far apart. [Hint: this is a collision problem (an explosion).]

Explanation / Answer

a) U(92, 238) ========> He(2, 4) + Th(90, 234)

Mass of Daughter nucleus = 234u

Charge = 90e

b) total electrostatic potential energy = kq1q2/r = (9*10^9*4*90*10^-38)/7.4*10^-15 = 4.38*10^-12 J

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