Topic 7: Atomic and nuclear physics 7.2 Radioactive Decay

3 hours

Radioactivity

• At the end of the 19th century and in the early part of the 20th, it was discovered, mainly due to the work of Henri Becquerel and Marie and Pierre Curie, that some nuclei are unstable. That is to say, nuclei spontaneously emit a particle or particles, they decay, and become different nuclui. This phenomenon is called redioactivity.

• There are three distinct emissions that take place, called alpha (a), beta (b), and gamma (g) radiations.

Antoine Henri Becquerel Pierre Curie Marie Curie, née

Sklodowska

1/2 of the prize 1/4 of the prize 1/4 of the prize

France France France

École Polytechnique Paris, France

École municipale de physique et de chimie industrielles (Municipal School of Industrial Physics and Chemistry) Paris, France

b. 1852d. 1908

b. 1859d. 1906

b. 1867(in Warsaw, Poland, then Russian Empire)d. 1934

1903 Nobel Prize in Physics

Awarded to Becquerel "in recognition of the extraordinary services he has rendered by his discovery of spontaneous radioactivity“ and to the Curie’s "in recognition of the extraordinary services they have rendered by their joint researches on the radiation phenomena discovered by Professor Henri Becquerel"

Ionization

• a, b, and g radiations ionize air as they pass through it; this means they knock electrons out of the atoms of the gases in the air.

• An a-particle of energy 2 MeV will produce about 10 000 ion pairs per mm along its air path. A b-particle of the same energy will produce about 100 ion pairs per mm and a g-ray about 1 ion pair per mm.

Three Distinct Emissions

• The existence of three distinct emissions is confirmed by letting these pass through a magnetic or electric field and observing the three separate beams.

Properties of a, b, and g RadiationsCharacteristic Alpha Particle (a) Beta Particle (b+, b-) Gamma Ray (g)

Nature Helium-4 Nucleus Fast Electron (or Positron)

Photon (high frequency EM radiation)

Charge +2e -e (or +e) 0

Mass 6.64 x 10-27 kg 9.1 x 10-31 kg 0

Maximum Speed ~0.06c ~0.98c c

Penetration Power A few cm of air or a thin sheet of paper

A few m of air or a few mm of metal

A few cm of lead

Detection Causes strong fluorescence

Affects photographic film

Is affected by electric and magnetic fields

Causes fluorescence

Affects photographic film

Is affected by electric and magnetic fields

Causes weak fluorescence

Affects photographic film

In not affected by electric and magnetic fields

Detecting Radiation: The Geiger-Müller Tube

• A Geiger–Müller tube consists of a tube filled with a low-pressure (~0.1 Atm) inert gas such as helium, neon or argon and an organic vapor or a halogen gas and contains electrodes, between which there is a potential difference of several hundred volts, but no current flowing. The walls of the tube are either metal or the inside coated with metal or graphite to form the cathode while the anode is a wire passing up the center of the tube.

• When ionizing radiation passes through the tube, some of the gas molecules are ionized, creating positively charged ions, and electrons. The strong electric field created by the tube's electrodes accelerates the ions towards the cathode and the electrons towards the anode. The ion pairs gain sufficient energy to ionize further gas molecules through collisions on the way, creating an avalanche of charged particles.This results in a short, intense pulse of current which passes (or cascades) from the negative electrode to the positive electrode and is measured or counted.

• Most detectors include an audio amplifier that produce an audible click on discharge. The number of pulses per second measures the intensity of the radiation field.

The Geiger-Müller Tube

The Geiger Counter

A.K.A.The Geiger

-Müller Detector

Detecting Radiation: The Ionization Chamber

• The ionization chamber is the simplest of all gas-filled radiation detectors, and is used for the detection or measurement of ionizing radiation. Conventionally, the term "ionization chamber" is used exclusively to describe those detectors which collect ion pairs from gases.

Smoke Detectors• The ionization chamber has found wide and beneficial

use in smoke detectors. In a smoke detector, the gap between the plates is exposed to the open air. The chamber contains a small amount of americium-241, which is an emitter of alpha particles. These alpha particles carry a substantial amount of energy, and when they collide with gas in the ionization chamber (mostly nitrogen and oxygen) the uncharged gas molecules will lose one or more electrons and become charged ions. Since the plates are at different voltages the ions and electrons will be attracted to the plates. The flow of ions between the plates represents a measurable current. If smoke enters the detector, it disrupts this current because ions strike smoke particles and are neutralized. This drop in current triggers the alarm.

Serge Plots• There are about 2500 nuclides (nuclei with

a specific number of protons and neutrons) but only about 300 of them are stable, the rest are unstable.

• As the number of protons in the nucleus increases the electrostatic repulsion between them grows, but the strong nuclear force does not grow proportionally since it is a short range force. Therefore extra neutrons must be added to increase the nuclear forces without participating in the repulsive electric force.

• However, too many neutrons will make the nucleus unstable and it will emit -aparticles to try and reach a more stable state.

Alpha Decay

• Alpha decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle, and thereby transforms (or 'decays') into an atom with a mass number 4 less and atomic number 2 less. We may express such a decay by the nuclear reaction equation:

Example of Alpha Decay

Beta Decay (A.K.A. Beta Minus Decay)

• In β− decay, the weak interaction converts a neutron (n) into a proton (p) while emitting an electron (e−) and an antineutrino (νe):

n → p + e− + νe

• The antineutreno is the antiparticle of a neutreno and is emitted in order to conserve momentum and energy. Neutrinos (meaning "small neutral ones") are elementary particles that often travel close to the speed of light, are electrically neutral, are able to pass through ordinary matter almost undisturbed and are thus extremely difficult to detect. Neutrinos have a minuscule, but nonzero mass. They are denoted by the Greek letter ν (nu).

Beta Decay (A.K.A. Beta Minus Decay)

• At the fundamental level (as depicted in the Feynman diagram to the right), this is due to the conversion of a down quark to an up quark by emission of a W− boson (an elementary particles that mediate the weak nuclear force); the W− boson subsequently decays into an electron and an antineutrino.

Beta Plus Decay (HL Only)

• In β+ decay, energy is used to convert a proton into a neutron, a positron (e+) and a neutrino (νe):

energy + p → n + e+ + νe

• So, unlike β−, β+ decay cannot occur in isolation, because it requires energy, the mass of the neutron being greater than the mass of the proton.

The Nuclear Reaction for b--Decay

• For example:

Gamma Decay

• Gamma rays are often produced alongside other forms of radiation such as alpha or beta. When a nucleus emits an α or β particle, the daughter nucleus is sometimes left in an excited state. It can then jump down to a lower level by emitting a gamma ray in much the same way that an atomic electron can jump to a lower level by emitting visible light or ultraviolet radiation.

Gamma Decay

6027 Co → 60

28 Ni* + e− + νe + γ + 1.17 MeV

6028 Ni* → 60

28 Ni + γ + 1.33 MeV

Gamma Ray Energies

• Typical gamma ray energies are in the mega electron volt (MeV) range and have a wavelength of

l = hc / DEwhere DE is the photon’s energy, h is Planck’s constant (6.63 x 10-34 J s) and c is the speed of light.

The Law of Radioactive Decay

• Radioactive decay is a random and spontaneous process and the rate of decay decreases exponentially with time. The law of radioactive decay states that the number of nuclei that will decay per second (i.e. the rate of decay) is proportional to the number of atoms present that have not yet decayed.

• There exists a certain interval of time, called the half-life, such that after each half-life the number of nuclei that have not yet decayed is reduced by a factor of 2.

Homework:

• Tsokos, Page 378, Questions 1 to 18