Radium dials (etc) - influence of closed or open source status on external dose rates

Radium dials

Dr Chris Robbins, Grallator

Introduction

Early to mid 20th century watch, clock, compass and aircraft instrumentation displays commonly used "radium dials" to create a self-luminous display without the need for either a back-light or an external "charging light". The luminous paint used was made by mixing a radium-226 (\(^{226}Ra\)) source with a phosphor such as zinc sulphide doped with trace metals and, in the day, hand painted on to the display.

The decay chain of \(^{226}Ra\) is shown below. The two nuclides shown in red boxes represent decay branches that occur very infrequently and these parts of the decay chain are ignored in this demonstration.

The \(\alpha\) (and \(\beta\) ) decays are primarily responsible for causing the phosphor to glow. The alpha radiation is effectively sheilded by the glass of the dial, however, there are still gamma emitters, principally \(^{214}Pb\) and \(^{214}Bi\) along to a lesser extent with \(^{226}Ra\) and \(^{210}Pb\), that are not effectively shielded.

It is interesting to note that the first decay daughter of \(^{226}Ra\), \(^{222}Rn\), is a gas rather than a solid, and this radon gas builds up inside the sealed instrument.

Secular equilibrium

The decay chain above shows that there is a large range of decay half live values with the largest being \(^{226}Ra\) at the head of the chain. The next nuclide in the chain is \(^{222}Rn\) which has a half life some 150,000 times shorter. This large difference means that the activity of \(^{222}Rn\),which is defined as the number of decays per second, is controlled by the activity of its parent, \(^{226}Ra\). Recall the decay constant of a nuclide \(i\), \(\lambda _i\) with a half life of \(t_{\frac{1}{2} i}\) as \(\lambda _i = \frac{\text{ln}(2)}{t_{\frac{1}{2} i}} \). For \(N_p\) moles of long-lived parent, the number of moles of a short-lived daughter, \(N_d\), when decay equilibrium has been established is given when the following is satisifed. \[ N_p \lambda _p = N_d \lambda _d \Rightarrow N_d = \frac{N_p \lambda _p}{\lambda _d} \] This state is an instantaneous equilibrium as \(N_p\) changes with time and is called a secular equilibrium.

The time for a parent to come into secular equilibrium with a parent is determined by the ratio of half-life values. For the complex decay chain of \(^{226}Ra\) there are several time scales over which secular equilibrium of activity is established. The interactive graph shown below shows these time scales based on the assumption of starting with a pure sample of \(^{226}Ra\). Note, the y-axis of this plot shows activity relative to the initial activity of the pure \(^{226}Ra\).

In this graph you can individually select and deselect nuclides by clicking on the relevant key entry on the right of the graph. The time scale of the plot can be changed by selecting the appropriate value on set of buttons at the bottom of the graph. Deselecting all the plots except \(^{226}Ra\) and \(^{222}Rn\) gives the following, where it is seen the activity of the two nuclides reach a secular equilibrium after about 30 days.

The daughters of \(^{222}Rn\) before \(^{210}Pb\) is reached all have shorter half-life values than \(^{222}Rn\) and so their secular equilibrium is determined by the first decay step of \(^{226}Ra\) to \(^{222}Rn\), which can be seen by selecting all the nuclides up to and including \(^{214}Po\), as shown below.

Note, the activity of \(^{214}Po\) will be slightly lower due to this branch being 0.99979 of all \(^{214}Bi\) decays. In fact the sum of the activity of \(^{214}Po\) and \(^{210}Tl\) (which will also be in secular equilibrium with \(^{214}Bi\)) will equal the activity of \(^{214}Bi\).

The nuclide \(^{210}Pb\) has a significantly longer half life than \(^{222}Rn\) and so will eventually come into secular equilibrium with \(^{226}Ra\). This process takes about 5 - 6 half lifes, so for \(^{210}Pb\) this is expected to be after ~120 - 150 years. Selecting "100 yrs" as the timescale of the graph shows how \(^{210}Pb\), and all its shorter-lived daughters approach, but don't quite reach, secular equilibrium over 100 years.

Breaking the glass / seal

Suppose now the glass containment of the instrument is broken and it is assumed all the radon gas escapes and further, that ongoing decay of \(^{226}Ra\) results in \(^{222}Rn\) which also escapes as a gas. In this case, the decay chain is effectively broken and all the daughters of \(^{222}Rn\) decay are without replacement. What are the radiological consequences?

The first consequence is that radon gas is now free to enter the environment and to be inhaled. The second consideration is what happens to the gamma dose rate. The interactive graph below helps answer this question.

Selecting the most important gamma emitters \(^{214}Pb\) and \(^{214}Bi\) along with the lesser ones \(^{226}Ra\) and \(^{210}Pb\), shows two sets of contributions to the gamma dose rate:

• The two major contributors to gamma dose rate decay to effectively zero after about 300 minutes (5 hours).
• The two minor contributors are more or less constant over a time period of 24 hours. In fact they will be more or less constant over many months as the half-life of \(^{226}Ra\) is 1,600 years and that of \(^{210}Pb\) is 22.3 years.

Radium dials (etc) - some further thoughts

Chris has clearly outlined what is going on in his interactive graphs and technical explanation. Before the interactive content we provided examples of radium dials and articles which yielded significant dose rates. We also noted that some of the dose rate was attributed to beta particles and their contribution will follow the same decay patterns noted above for gamma rays. 

What has been presented so far are the two extremes:  closed (sealed) or open (unsealed). In reality it is possible that an article might follow something between the two. We have noted this for certain stored specimens in museums where there is a very localised increase in radon measured in air (i.e. Bq/m³) which cannot be explained by natural radon sources (i.e. radon seeping up from below ground). When dose rate monitoring such specimens it explains why there are hot and cooler samples of what appear to be very similar articles. A closer inspection often reveals that the higher dose rate article appears in better condition, where as the lower dose rate (cooler) article often has cracks in the glass front. Clearly for the damaged article there is an ongoing partial leak of radon and therefore the activity of the progeny is less (and hence also is the dose rate).  

Gamma dose rates from sealed radium sources

You can use various Ionactive calculators to estimate the gamma dose rate from a sealed (closed) source of radium if the activity is known or can be estimated. More likely, you can use the same calculator resource in reverse to estimate the activity if you know the dose rate. In our experience, the dose rates we took from radium dials / articles featured in this resource are extreme cases (see  the  below for a reminder). 

For dose rates of this magnitude you can probably take a useful measurement further away (10's cm) which will both approximate the item to a point source, and avoid detection of most of the betas (i.e. leaving a true gamma dose rate). An alternative to this, and this would be especially useful for much lower dose rates, is to use some acrylic material 5-10mm thick to shield the betas such that dose rates can be taken nearer the item (which may be necessary anyway for lower dose rates). 

When you have a suitable measurement you can then use some of the Ionactive calculator resource such as this: Dose Rate to Radioactivity Calculator (with optional shielding). Note that the Ra-226 selection on this calculator specifically states that this is in the form of a sealed source.  

Taking the value of 860 micro Sv/h (at 2 cm given the picture above) you will note that the potential radium activity might be up to to 2 MBq (give it a try at the above link). Noting earlier it was suggested that 40-50% of the dose rate could be betas, then our activity estimate is probably on the high size. That said, if Rn-222 is partially leaking from the source in some way, then this might suggest our measured dose rate could underestimate the activity. With these unknowns we will stick with the 2 MBq Ra-222 estimate. 

From a casual search across the internet 2 MBq is on the high side, then again this is being compared to watches and compasses, whereas our example is from the rather unique Vickers Valiant B1. We have noted that some watches may yield up to 30 micro Sv/h at 2 cm from the surface. If these values are plugged into our linked calculator it yields about 66 kBq of radium-226 which is within the region of the reported values (but noting our comment on beta dose rate). A better estimate for a watch could be made by measuring through the back - the dose rate will be lower as many of the betas will then be shielded (or use the acrylic as suggested earlier). 

Do you keep radium dials (watches etc)?

Have you noticed a recent drop in dose rate (or count rate if you are perhaps using a consumer grade counter)? If you have, this could be due a break in containment (carefully look for signs of damage). The issue is you could be moving from a sealed (closed) source situation to an unsealed (open) source. Leaking Ra-226 is potential problem, radium is an alpha emitter and you do not want to be inhaling or ingesting it. If in doubt seek the advice of a Radiation Protection Adviser.