Binding Energy (II) What is the maximum KE of the emitted βparticle during the decay of 27^60 C

Binding Energy (II) What is the maximum KE of the emitted...

Key Concepts

Energy Conservation in Nuclear Reactions

Energy conservation in nuclear reactions mandates that the total energy before and after the decay remains constant. In beta decay, this means that the energy released (Q-value) is partitioned between the kinetic energy of the beta particle, the neutrino, and the recoil energy of the daughter nucleus. The maximum kinetic energy of the beta particle is observed when the neutrino carries away minimal energy.

Q-value (Decay Energy)

The Q-value is the net energy released during a nuclear reaction, calculated from the mass difference between the initial and final states according to the principle of mass-energy equivalence. In beta decay, the Q-value represents the total energy available to be shared among the emitted beta particle, the neutrino, and the recoil of the daughter nucleus.

Beta Decay

Beta decay is a type of radioactive decay in which an unstable nucleus transforms one of its neutrons into a proton (or vice versa) while emitting a beta particle, which is an electron or positron. This process changes the atomic number of the nucleus and involves the conversion of nuclear energy into the kinetic energy of the emitted beta particle and, sometimes, neutrinos.

Binding Energy

Binding energy refers to the energy that holds a nucleus together. It is the energy required to separate the nucleus into its individual protons and neutrons. In the context of nuclear decay, differences in binding energy between the parent and daughter nuclei contribute to the energy release observed in the emitted particles.

Transcript

00:01 In this question, we've been asked to find the maximum kinetic energy of a beta minus a particle that is emitted when cobalt 60 decays under beta minus decay.

00:17 So this is what we begin with, cobalt 60, which has 27 protons.

00:24 So to answer this question, what i'm going to do is first write down the decay equation.

00:28 And from the decay equation, we can then use the masses prior to the decay and after the decay.

00:36 And if we take these away from each other, this mass difference can be converted into an energy using e equals mc squared.

00:43 And this energy is equal to the maximum kinetic energy of the emitted beta particle.

00:52 In beta minus decay, we have a neutron converting into a proton.

00:59 So our number of protons is going to increase to 28, but our number of nucleons remains the same.

01:05 And the atom with 28 protons is nickel.

01:09 So this is nickel.

01:11 We then have our beta minus particle and a neutrino.

01:17 Now the maximum kinetic energy of our beta minus particle is going to occur when we actually have no neutrino emitted.

01:26 So i'm just going to rub this away.

01:27 And now what we are going to do is we're going to take the mass of the cobalt 60, so m -cobalt, and from that we're going to take away the mass of the nickel and the mass of the beta particle, and then convert this into an energy by timesing by c squared...

Please give Ace some feedback