Isotopes & Radioactive Decay (HL IB Physics)

• Elements are defined by a fixed number of protons in their atoms
  • For example, all hydrogen atoms have 1 proton, and all carbon atoms have 6 protons

• However, atoms of an element can have different numbers of neutrons
  • These different versions of elements are called isotopes

• An isotope is defined as:

Nuclei that have the same number of protons but different numbers of neutrons

• For example, hydrogen has two isotopes, deuterium and tritium
  • All three isotopes contain 1 proton, but different numbers of neutrons

The three atoms shown above are all forms of hydrogen, but they each have different numbers of neutrons

• Since nucleon number A includes the number of protons and neutrons, an isotope of an element will have
  • A fixed proton number, Z
  • A different nucleon number, A

• Some isotopes have an imbalance of neutrons and protons which makes them unstable
  • This means they constantly decay and emit radiation to achieve a more stable form
  • This can happen from anywhere between a few nanoseconds to 100,000 years

Differences between isotopes

• The number of neutrons in an atom does not affect the chemical properties of an atom, such as its charge, but only its mass
  • This is because neutrons have no charge but do have mass

• The charge of the nucleus of a particular element is always the same
• In the periodic table, the mass number of Chlorine is often given as 35.5

This section of the periodic table shows chlorine as having a mass number of 35.5, but other elements have an integer mass number

• The mass number of Chlorine is given as 35.5 because it has two isotopes with mass numbers of 35 and 37, and these occur in a ratio of 3:1 respectively so 35.5 is the average nucleon / mass number
• The number of electrons and protons in different isotopes remains the same
• Less common isotopes tend to be more unstable due to the imbalance of protons and neutrons

Isotopic Data

• Isotopic data is defined as:

The relative amounts of different isotopes of an element present within a substance

• The mass of an element is often given as relative atomic mass
• The relative atomic mass of an element can be calculated using the relative abundance values
• The percentage abundance of different isotopes in a sample can be obtained using a mass spectrometer

Table of isotopic data for a sample of oxygen

• For example, a sample of oxygen may contain three isotopes: ,  and 
• The relative abundance of this sample of oxygen can be calculated using:

(16 × 0.9976) + (17 × 0.0004) + (18 × 0.002) = 16.0044

• To two decimal places, the relative abundance of the sample of oxygen is 16.00

• A common use of isotopic data is carbon dating of archaeological artefacts 
  • This involves using the ratio of the amount of stable isotope carbon-12, to the amount of unstable isotope, carbon-14
  • The age of a sample of dead tissue can be determined by comparing the ratio of these isotopes to the ratio in a sample of living tissue

• Radioactive decay is defined as:

The spontaneous disintegration of a nucleus to form a more stable nucleus, resulting in the emission of an alpha, beta or gamma particle

• The random nature of radioactive decay can be demonstrated by observing the count rate of a Geiger-Muller (GM) tube
  • When a GM tube is placed near a radioactive source, the counts are found to be irregular and cannot be predicted
  • Each count represents a decay of an unstable nucleus

• These fluctuations in count rate on the GM tube provide evidence for the randomness of radioactive decay

The variation of count rate over time of a sample radioactive gas. The fluctuations show the randomness of radioactive decay

Characteristics of Radioactive Decay

• Radioactive decay is both spontaneous and random
• A spontaneous process is defined as:

A process which cannot be influenced by environmental factors

• This means radioactive decay cannot be affected by environmental factors such as:
  • Temperature
  • Pressure
  • Chemical conditions

• A random process is defined as:

A process in which the exact time of decay of a nucleus cannot be predicted

• Instead, the nucleus has a constant probability, ie. the same chance, of decaying in a given time
• Therefore, with large numbers of nuclei, it is possible to statistically predict the behavior of the entire group