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Weighing out Tc-99m (No thank you)

Dear Reader,

I have to ask the question of should I teach chemistry using problems based on reality ? Now I do not know how many of you have considered what teaching and learning events are, I would argue that any event which has the potential to improve the knowledge or skills of the student is a teaching event. Regardless of whether I am present or not, a moment when a student is studying is a teaching event.

Now then we need to consider the question of should I always base a teaching event on real life, the advantage of basing it on real life using real data is that we will be more sure that we are not teaching students wrong things. There is the worry that sometimes the data collected during real life events is incomplete or even wrong, but our general hope is that by teaching from real life that we can make sure that we teach relevant and correct things to the students.

On the other hand we can teach using science fiction scenarios, for example I once set an exam question where the students had to make calculations which relate to radioactive waste disposal from the point of view of an alien on a far away planet. This alien had to do radioactive decay calculations which are similar to those done on earth by humans so I would argue that the question is still relevant. While none of my students life on planet Zxef the calculation does test their ability to do a set of calculations which are of use on earth. For example shortly after the Fukushima event a measurement of 239Np in environmental samples was made, one of the people in nuclear chemistry grabbed his calculator and then estimated the activity released on the first day.

A favourite of mine is a homework in organic chemistry where students have to do Indiana Jones temple of doom themed problems, if you get a problem wrong the worksheet describes a range of horrible adverse health effects such as being showered in boiling oil or being attacked by a dire polyol monster which will hydrogen bond all the water molecules in your body at once. The students typically laugh and then enjoy themselves doing problems which if presented in a dry way without the humour would be viewed as boring problems.

Now I sincerely hope that one of my students make the mistake of thinking that I am in communication with aliens or that I raid temples looking for interesting artefacts. But there is a problem with a type of teaching event which is not based on real life but at appears to be based on real life. These problems in some books are based on a distorted version of real life which does not warn the reader that real life has been simplified or distorted in some way.

For example the question

Gamma rays obey the Beer-Lambert rule (I = Io e-kx), so given that k = 0.9 cm-1 then calculate the thickness of lead required to reduce the radiation level by a factor of 100.

Is a bad question as depending on the geometry this calculation can give a misleading answer, while for a lead wall intended to attenuate a broad beam of gamma rays (they are parallel) it will work. It will not work for working out the thickness of lead required for a spherical shield to hold a gamma ray source. Here scattering effects such as Compton scattering make the problem more complex. Also the scattering effects help the gamma rays to escape from the lead block so the real thickness needs to be larger. A better question in an exam on radiological protection would be

Ignoring scattering effects known as buildup, if the attenuation coefficient (k = 0.9 cm-1) then calculate the thickness of lead required to reduce the radiation level by a factor of 100.

Here there is less danger that the exam will install in the minds of the students some oversimplification of the problem. A worse type of teaching example is one in which two or more effects operate on a system and one major effect tends to counteract at least one of the other major effects, when the question ignores one of the effects. For example consider the following

As the electronegativity of the chalcogens decreases as their atomic number increases, put the following acids in order of acidity.

H2O, H2S, H2Se and H2Te

While I can not recall the pKa for H2Se and H2Te I can tell you that an argument about the acid strength of these compounds based only on electronegativity will give the wrong answer. Water is a weaker acid than hydrogen sulfide because the extremely high bond energy of the O-H bond makes water less able to dissociate to form H+ and OH than H2S is able to dissociate to form H+ and SH.

A still worse example is a question which totally distorts reality. For example

A 100 mg sample of 99mTc is placed on a truck, as the half life of this nuclide is 6 hours calculate how much is left when it arrives 9 hours later at a remote hospital.

The problem with this question is that it is a gross distortion of real life, firstly if I was to make a sample of a 99mTc compound such as solid KTcO4, ignoring radiolysis, then the mass and form of the sample would not change with time. The metastable state of 99mTc would change in to the ground state thus forming 99Tc.

Secondly no person in their right mind (or otherwise) would attempt to make and transport 99mTc to a hospital in a weighable amount. We can calculate the activity of the sample.

One curie is the activity of one gram of 226Ra, this isotope of radium has a half life of 1600 years (14025600 hours). So we can instantly see that the decay rate of our 99mTc is much higher than that of radium. Now trust me a 1 Ci radium-226 source is a real beast of a radioactive monster, you would not want to handle it without a long pair of tongs ! and some heavy shielding as well for long jobs.

Now lets calculate the activity of the 100 mg of 99mTc, we have 1.01 mMoles of the nuclide present.

Now that is 606060606060606060606 atoms, which is 6.06 x 1020 atoms.

We can use the following equation

A = Nl

Where l = ln(2)/t½

As the half life is 21600 seconds

Then l = 3.209 x 10-5 seconds-1

So we have 1.945 x 1016 Bq of activity

In the olde units of curies this is 525637 curies or 525 kCi

Now I can tell you that this amount of a gamma emitter is in the range which could cause instant death if you go near it, I know that a shielded container would be needed to transport it. I know that a classic gamma irradiation machine with 6000 Ci inside of 60Co has about three tonnes of lead shielding on it, even then the dose rate near such a machine is quite a bit above background. While the amount of lead per unit of activity will be lower (the photon energy of 99mTc is lower at 140 keV than that of 60Co).

Also to work with this amount of radioactivity you would need a hot cell, also the dose rate near the lump of 99mTc would be very high.

We can calculate the dose rate using the activity to dose coefficient of 0.076 rads per hour at one meter from one curie. So our monster source will deliver 39948,42 rads per hour at one meter. Which is 399 Gy per hour. So this will be a major problem with a typical modern electronic balance, at 10 cm it will give a dose rate of 39948 Gy per hour.

The half value thickness for lead with this gamma emitter is 0.027 cm, so attenuation constant is 25.67 cm-1.

If we assume that the dose rate at 1 meter should be only 2.5 microGy per hour, then we will need a protection factor of 160 x 106. This will require 0.736 cm of lead.

The problem is that the surface dose rate will be about 46 mGy per hour at the surface. This is far too high, so we would have two choices. Either the source could go into the centre of a 2 meter cube crate, or we could choose a thicker lead pot.

If we choose a 2.5 microGy per hour at 5 cm then this will require a 400 times higher attenuation. This will require 1 cm of lead. This will require a box which is a 10 cm cube.

Well back to that question, I think that the idea of trying to weight out 100 mg of Tc-99m is plain crazy and bonkers, a better question would be

a person puts in the boot of their car 1 GBq of Tc-99m and drives for 9 hours to a hospital, how much radioactivity will remain when they arrive ?

This would be more reasonable in terms of how people work with radioactivity.

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