Studio Session 13

Nuclear decay and MRI

Radioactive nuclei spontaneously decay.  The decay of an unstable nucleus is a quantum process.  The probability that a given nucleus will decay in the next time interval Δt is independent of the history of the nucleus.  The decay process is entirely random, and it is impossible to predict when a particular nucleus will decay.  The decay constant λ of a nucleus is its decay probability per unit time.  The probability that the nucleus will decay in the next small time interval Δt is λΔt.

Starting with a large number N0 of radioactive nuclei at t = 0, we find that the number still present at time t is well approximated by a function representing exponential decay.

N(t) = N0exp(-λt).

The mean lifetime of the nuclei is given by τ = 1/λ, and the half-life is given by t½ = τ ln2 = ln2/λ.

Open a Microsoft Word document to keep a log of your procedures, results and discussions.

Experiment 1:

In this experiment you will simulate the decay of radioactive nuclei by rolling dice.  You will start the experiment standing upright, representing a radioactive nucleus before its decay.  You will sit down when the nucleus you are representing decays.  Whether the nucleus you represent decays or not, will depend on the roll of a die.

Experimental procedure:

Before the experiment starts, download the linked spreadsheet and open it so you can enter data. 
In this experiment all students have to participate.  Your instructor will be the conductor.

Data analysis:

How does this experiment simulate nuclear decay?  Discuss this with your group members.

Exploration 1:

Some nuclear reactions do not occur spontaneously, but require external sources of energy, in the form of "collisions" with outside particles.  "Activation energy" has to be provided before a much larger amount of "reaction energy" is released.   Nuclear fission can be "activated" when a slow neutron collides with a fissionable nucleus.

You will use an on-line simulation from the University of Colorado PhET group to explore nuclear fission.
Link to the simulation

Click the Fission: One Nucleus tab.

Click the Chain Reaction tab.

Click the Nuclear Reactor tab.

Watch the linked video.  Is this a good analogies of a nuclear chain reaction?  If mousetraps and Ping-Pong balls are used to illustrate a fission chain reaction, what do each represent?

Exploration 2:

Use an on-line simulation from the University of Colorado PhET group to explore a simplified version of NMR and MRI.
Link to the simulation: 
Click "Run Now!" or "Download".

Start with the simplified NMR simulation.

Nuclei g (MHz/T) from notes g = f/B  from your measurements
1H 42.58  
23Na 11.27  

Paste your table into your word document and briefly discuss your results.

Switch to the MRI simulation.

Convert your log into a session report, certify with you signature that you have actively participated, and hand it to your instructor.