Nuclear Excited States (AQA A Level Physics)

Revision Note

Katie M

Author

Katie M

Last updated

Nuclear Excited States

  • A nucleus can exist in an excited state in the same way as an electron

  • Once an unstable nucleus has decayed, it may emit any remaining energy in the form of a gamma photon (γ)

    • The emission of a γ photon does not change the number of protons or neutrons in the nucleus, it only allows the nucleus to lose energy

  • This happens when a daughter nucleus is in an excited state after a decay

  • This excited state is usually very short-lived, and the nucleus quickly moves to its ground state, either directly or via one or more lower-energy excited states

Technetium Production, downloadable AS & A Level Physics revision notes

Metastable technetium-99m is a technetium-99 nucleus in an excited energy state

  • One common application of this is the use of technetium-99m as a γ source in medical diagnosis

    • The ‘m’ stands for metastable which means the nucleus exists in a particularly stable excited state

  • Technetium-99m is the decay product of molybdenum-99, which can be found as a product in nuclear reactors

  • The decay of molybdenum-99 is shown below:

Mo presubscript 42 presuperscript 99 space rightwards arrow space Tc presubscript 43 presuperscript 99 straight m end presuperscript space plus space straight beta presubscript negative 1 end presubscript presuperscript 0 space plus space top enclose v subscript e

Tc presubscript 42 presuperscript 99 straight m end presuperscript space rightwards arrow space Tc presubscript 43 presuperscript 99 space plus space straight gamma

  • The half-life of molybdenum-99 is 66 hours

    • This is long enough for the sample to be transported to hospitals

    • Subsequently, the technetium-99m can be separated at the hospital

  • Technetium-99m has a short half-life of 6 hours

    • This is an adequate timeframe for examining a patient

    • Plus, it is short enough to minimise damage to the patient

Nuclear Energy Level Diagrams

  • Nuclear energy levels are similar to electron energy levels

  • The nuclear energy level diagram of molybdenum-99 can be represented as follows:

Nuclear Energy Level Tc99, downloadable AS & A Level Physics revision notes

An excited molybdenum-99 nucleus undergoes beta decay into metastable technetium-99m which is a gamma emitter with a half-life of 6 hours

  • The decay mode (usually alpha or beta) is represented by a diagonal line

  • The excited state, or states, are generally stacked in descending energy order to the right of the decay

Worked Example

A nucleus of iron Fe-59 decays into a stable nucleus of cobalt Co-59. It decays by β emission followed by the emission of γ-radiation as the Co-59 nucleus de-excites into its ground state.

The total energy released when the Fe-59 nucleus decays is 2.52 × 10–13 J.

The Fe-59 nucleus can decay to one of three excited states of the cobalt-59 nucleus as shown below. The energies of the excited states are shown relative to the ground state.

WE - Nuclear Energy Levels, downloadable AS & A Level Physics revision notes

Following the production of excited states of Co-59, γ-radiation of discrete wavelengths is emitted.

(a) Calculate the maximum possible kinetic energy of the β– particle emitted in MeV.

(b) State the maximum number of discrete wavelengths that could be emitted.

(c) Calculate the longest wavelength of the emitted γ-radiation.

Answer:

Part (a)

Step 1: Identify the beta emission with the largest energy gap

WE - Nuclear Energy Levels Ans a, downloadable AS & A Level Physics revision notes

Step 2: Calculate the energy difference

ΔE = (2.52 – 1.76) × 10–13 = 7.6 × 10–14 J

Step 3: Convert from J to MeV

  • 1 MeV = 1.6 × 10–13 J

Part (b)

WE - Nuclear Energy Levels Ans b, downloadable AS & A Level Physics revision notes
  • There are 6 possible transitions, hence 6 discrete wavelengths could be emitted

Part (c)

Step 1: Identify the emission with the longest wavelength / smallest energy gap

WE - Nuclear Energy Levels Ans c, downloadable AS & A Level Physics revision notes
  • Longest wavelength = lowest frequency = smallest energy

Step 2: Calculate the energy difference

ΔE = (2.29 – 2.06) × 10–13 = 2.3 × 10–14 J

Step 3: Write down de Broglie’s wavelength equation

Where:

  • h = Planck’s constant

  • c = speed of light

Step 4: Calculate the wavelength associated with the energy change


You've read 0 of your 5 free revision notes this week

Sign up now. It’s free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

Did this page help you?

Katie M

Author: Katie M

Expertise: Physics

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.