Question

1. In the search for a site for the disposal of radioactive waste, a stringent requirement has been imposed, which is that the waste should not have a chance to leak out for at least 10,000 years. What do you think sets this age scale?

2. By looking up the masses of the neutron, proton, and electron, find the maximum energy, in MeV, of an electron produced in the decay of a neutron (i.e. one neutron decays to a proton, electron and electron neutrino). (Answer: 0.784 MeV)

3.The carbon cycle, a stellar burning process secondary to the proton cycle, consists of the following sequential series of nuclear reactions and decays:
12C + p → 13N + γ, with 1.9 MeV of energy released;
13N → 13C + e+ + v, with 1.2 MeV of energy released;
13C + p → 14N + γ, with 7.6 MeV of energy released;
14N + p → 150 + γ, with 7.4 MeV of energy released;
15O → 15N + e+ + v, with 1.7 MeV of energy released;
15N + p → 12C + 4He, with 5.0 MeV of energy released.
(a) What is the net effect of one cycle, and how much energy is produced per cycle?
(b) Consider a star of mass 3·1030 kg, consisting mainly of hydrogen, with 0.1 percent of its mass in 12С. The characteristic duration of a carbon cycle in the star is 5·106 yr. Estimate the energy produced each year by the carbon cycle, assuming that each carbon nucleus in the star acts as a catalyst for the cycle.
(Answer: (a) 24.8 MeV released, (b) 7.5·1047 MeV (1.2·1034 J).)

Answer 1

1) Nuclear waste produced remain radioactive for thousands of years. For example, 56,000 curies radioactivity of isotope Pu -239 remain even after 10,000 years for 1000 tons of fuel spent.

2)n→ p+ e⁻+ ν_e^-

Mass of antineutrino < 0.120 x 10^-6 MeV/c².

Mass of neutron = 939.5654 MeV/c²

Mass of electron = 0.5110 MeV/c²

Mass of proton = 938.2721 MeV/c²

Energy released = Mass difference x c²

= [mass of neutron - ( mass of proton + mass of electron + mass of antineutrino)] x c²

=   [939.5654 - ( 938.2721 + 0.5110 + 0.120 x 10^-6) ] x c²

= [0.7823 MeV/c²] xc²

   0.7823 MeV