Radioactive Decay (Cambridge (CIE) IGCSE Physics): Revision Note

Effect of nuclear size on decay

Extended tier only

• Isotopes of an element may be radioactive due to an excess of neutrons in the nucleus and/or the nucleus being too heavy

Excess of protons or neutrons

• The most stable nuclei have roughly the same number of protons as neutrons, especially among light elements

• In heavier nuclei, stability requires more neutrons than protons because neutrons help reduce the electrostatic repulsion between positively charged protons by contributing to the strong nuclear force

• If a nucleus has too many or too few neutrons relative to protons, it becomes unstable and may decay into a more stable nucleus by releasing radiation

• An example of this is the isotope of hydrogen–1

  • H-1 is the stable nucleus of hydrogen with 0 neutrons and 1 proton

  • H-2 (deuterium) has one more neutron in the nucleus

  • H-3 (tritium) has 2 neutrons to 1 proton. This is much more unstable than H-1 or H-2

Hydrogen isotopes

Heavy nucleus

• If a nucleus is too heavy, this means it has too many protons and neutrons

  • The forces keeping the protons and neutrons together in the nucleus will be weaker

• An example of this is uranium–238

  • It has a nucleus with 238 protons and neutrons

• During nuclear decay, the mass number of the element which it decays into is gradually reduced

  • This is done through alpha (α) or beta (β) decay

Uranium–238 decay chain

The graph shows the decay chain of uranium-238 through alpha and beta emission

Change to a new element

• A nucleus changes to a different element, during α-decay or β-decay

  • The initial nucleus is often called the parent nucleus

  • The nucleus of the new element produced is often called the daughter nucleus

• The daughter nucleus is a new element because it has a different proton and/or nucleon number than the original parent nucleus

• This can be seen on a graph of N (neutron number) against Z (proton number)

  • For example; when Pu-239 decays by alpha to U-235, it loses 2 protons and 2 neutrons

  • U (uranium) is a completely different element from Pu (plutonium)

Graph of neutron number against proton number

Graph of N against Z for the decay of Pu–239

Reducing neutron number

Extended tier only

• α and β-decay affect the nucleus by

  • increasing its stability

  • reducing the number of excess neutrons

Alpha decay

• During alpha decay an alpha particle is emitted from an unstable nucleus

• A completely new element is formed in the process

Alpha decay

Alpha decay usually happens in large unstable nuclei, causing the overall mass and charge of the nucleus to decrease

• An alpha particle is a helium nucleus

  • It is made of 2 protons and 2 neutrons

• When the alpha particle is emitted from the unstable nucleus, the mass number and atomic number of the nucleus changes

  • The mass number decreases by 4

  • The atomic number decreases by 2

• The charge on the nucleus also decreases by 2

  • This is because protons have a charge of +1 each

Beta decay

• During beta decay, a neutron changes into a proton and an electron

  • The electron is emitted and the proton remains in the nucleus

• A completely new element is formed because the atomic number changes

Beta decay

Beta decay often happens in unstable nuclei that have too many neutrons. The mass number stays the same, but the atomic number increases by one

• A beta particle is a high-speed electron

• It has a mass number of 0

  • This is because the electron has a negligible mass, compared to neutrons and protons

• Therefore, the mass number of the decaying nucleus remains the same

• Electrons have an atomic number of -1

  • This means that the new nuclei will increase their atomic number by 1 so atomic number is conserved before and after the decay

Gamma decay

• During gamma decay, a gamma ray is emitted from an unstable nucleus

  • This process makes the nucleus less energetic but does not change its structure because gamma radiation has no mass or charge

Gamma decay

Gamma decay does not affect the mass number or the atomic number of the radioactive nucleus, but it does reduce the energy of the nucleus

Decay equations

Extended tier only

• Decay equations, use nuclide notation, to show the emission of α-particles, β-particles and γ-radiation

• A decay equation is similar to a chemical reaction equation

  • The particles present before the decay are shown before the arrow

  • The particles produced in the decay are shown after the arrow

• During decay equations, the sum of the mass and atomic numbers before the reaction must be the same as the sum of the mass and atomic numbers after the reaction

Alpha decay equation

• All alpha decay equations have the following form for isotopes X and Y:

${}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{X}\to {}_{\mathrm{Z}-2}{}^{\mathrm{A}-4}\mathrm{Y}+{}_2{}^4\mathrm{\alpha }$

• The following decay equation shows polonium-212 undergoing alpha decay

  • It forms lead-208 and an alpha particle

  • An alpha particle can also be written as a helium (He) nucleus 

  ${}_{84}{}^{212}\mathrm{Po}\to {}_{82}{}^{208}\mathrm{Pb}+{}_2{}^4\mathrm{\alpha }$

Beta decay equation

• All beta decay equations have the following form for isotopes X and Y:

${}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{X}\to {}_{\mathrm{Z}+1}{}^{\mathrm{A}}\mathrm{Y}+{}_{-1}{}^0\mathrm{\beta }$

Gamma decay equation

• All gamma decay equations have the following form for isotope X

${}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{X}\to {}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{X}+{}_0{}^0\mathrm{\gamma }$