Trent Physics 203H Lab Neutron Activation and Radioactive Decay Neutron Activation and Radioactive Decay

Introduction

In this experiment indium foils are activated by irradiation with thermal neutrons. The resulting radioactivity is measured as a function of irradiation time and the decay of the radioactivity after irradiation is followed to find the half-life of a metastable state of In116 .

Theory

Only a small fraction of the known isotopes are stable. Some unstable naturally occurring isotopes (e.g. 40K, uranium isotopes, etc.) appear stable but actually have very long half-lives ( ≈ 109 years). Often unstable isotopes can be made by irradiating stable elements. A common method of producing radioactive isotopes is by neutron activation: the addition of an extra neutron forms a heavier isotope which is (usually) unstable against radioactive decay.

In this experiment foils of the stable element 49 In115 are bombarded by neutrons produced in a radioactive source (described below). The reaction is

0 n1 + 49 In115 →49 In116,m

The m indicates that the In116 nuclei are formed in metastable states. These states could in principle decay by prompt emission of gamma rays leading to lower excited states of In116 . Normally such gamma emission would very quickly leave the nucleus in its ground state which could then decay by β − emission to states of 50 Sn116 . However the first excited state of In116 has a very low probability of gamma-emission. This is because it is only slightly more energetic than the ground state (0.127 MeV) and the difference in spins is + + rather large (5 →1 ). Therefore this state decays instead by β − emission to excited states of 50 Sn116 . The half-life for this decay is about 54 minutes.

The amount of radioactivity produced by a foil bombarded with neutrons depends on the number of atoms of the required type in the foil, the probability of absorption of a neutron by the foil, and the flux of neutrons incident on the foil. Let P be the rate of production of radioactive atoms (per second). The atoms formed are unstable and decay with a half life τ. The number decaying in 1 second is proportional to the number N present. Therefore, the change in the number of radioactive atoms per unit time is dN = −λN + P (1) dt where, from the definition of half-life ln2 λ = (2) τ

Solving differential equation (1) with the boundary condition that no radioactive atoms were present initially, the number of atoms present after an exposure time te is

1 Trent Physics 203H Lab Neutron Activation and Radioactive Decay P N(t ) = (1− e −λte ) (3) e λ

Sketch N(te) as a function of te and include this in your laboratory report.

If one wishes to measure the radioactivity induced, the sample is withdrawn from the neutron source and placed in a counter which detects the gamma rays emitted. The number of disintegrations per second is equal to λN , but the detector efficiency is less than 1 (say k), so the measured number of counts per second is the activity:

−λte A(te ) = kλN(te ) = kP(1− e ) (4)

This is the activity that would be measured immediately after exposure. In practice, a finite time, tw, elapses between the end of the exposure and the beginning of the activity measurement. Moreover the activity is not measured instantaneously, but counts are accumulated for a finite time tc. The number of counts recorded will be given by:

tw +tc C = A(t )e−λt dt ∫ e (5) tw By doing this integral show that: λCeλtw A(te ) = (6) 1− e−λtc

You should include this derivation as an appendix in your lab report – either handwritten or using a word processor’s Equation Editor.

Apparatus

Neutron Source:

The irradiation facility provided is called a neutron howitzer. It consists of a radioactive neutron source in a tank of water. The neutron source consists of a quantity of plutonium intimately mixed with beryllium. Alpha particles emitted by the radioactive plutonium interact with beryllium nuclei to produce fast neutrons ranging in energy up to 10 or 12 MeV. The probability of neutron absorption by indium is largest for "thermal neutrons" (energy of the order of 1/40 eV). The water in the tank serves as a moderator - the energies of the neutrons are reduced, by successive collisions with hydrogen nuclei, to thermal energies.

Racks are provided for lowering the indium foils to a position near the neutron source. For each irradiation a foil is inserted in a slot in the rack which is then lowered to a platform in the tank. After the desired exposure time the rack is withdrawn and the foil may be removed for activity determination. The irradiated foil MUST be handled with tweezers. To protect the soft metal of the foil, wrap the ends of the tweezers with tape.

NOTE: The neutron source is very radioactive and must not be removed from the water tank. The water in the tank serves as an adequate shield but it is only common sense to keep your radiation exposure to a minimum by staying away from the tank except when the sample is being inserted or removed. The room in which the source is stored must be locked unless someone is present in the adjacent laboratory.

2 Trent Physics 203H Lab Neutron Activation and Radioactive Decay

Counting Apparatus:

A scintillation detector (NaI-Tl) is provided. For each activity measurement, the radioactive foil is to be placed near the detector in such a manner that the detector efficiency k will be the same for each measurement. The amplifier output from the detector system is fed to a single channel analyzer (SCA) and scalar, and also to a multichannel analyzer so that the spectrum of the radioactive source may be observed.

Experiments:

A: An indium foil has been placed in the tank for an irradiation time of a few hours. The instructor will remove this foil and prepare it for counting.

Examine the spectrum of the emitted gamma rays and be sure that the amplifier gain is set so that most of the radiation results in pulses less than 10 V in height. (Full scale on the PHA corresponds to 10 V.) Remove the radioactive foil (using tweezers) and examine the spectrum of the background radiation. Much of this is low energy gamma rays. You can avoid counting them by adjusting the baseline of the SCA to the level indicated by the PHA spectrum. When this has been done measure the background count rate.

Return the activated foil to the counter. At 5 minute intervals record the counts for a fixed time (30 sec or 1 min). Continue for about two half-lives. Correct the activity for background.

Construct a plot of ln(counts) versus time. The points should fall on a straight line whose slope is -λ where λ = ln2 /τ . Hence determine the half-life of the radioactivity. This is the half-life of the first excited state of the In116 nucleus.

B: Several indium foils are provided, each with its mass (accurate to 0.1 mg) stamped on them.

Place a foil in a slot in the rack provided. (Mark the slot so that the same one is used each time.) Carefully but quickly lower the rack onto the platform in the water tank, placing the foil as close to the neutron source as possible. Start a stopwatch as soon as the foil is in position. After a time te has elapsed, remove the rack. Use tweezers to take the foil (it may be dried by patting it with a paper towel) to the counting apparatus. Start the counter when a fixed time tw (1 minute should be long enough) has elapsed since removing the foil from the tank. Count for a fixed time, tc, e.g. 1 minute . Correct the counts for background and standardize to a foil mass of 1 g. Use equation (6) to calculate the activity A(te).

This should be done for exposure times te = 2, 5, 10, 20, 35, 60 and 120 minutes. Plot A(te) versus te.

Questions:

1. What is the maximum activity obtainable? Why is it limited? Why doesn’t it just keep increasing? 2. There are two naturally occurring isotopes of indium (95.7% In115 , 4.3% In113 ). What is the justification for neglecting activity induced in the lighter isotope?

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