Simulating the Half Life of a Radioisotope

Australian Curriculum and Year 9 "Science"

 Last year I was writing questions for an Australian Years 9-10 Science textbook when I first came across the "gamma decay" problem.

The textbook authors stated that there are 3 types  of radioactive decay: alpha, beta and gamma (which is kind of OK for Year 9 or 10 science). They wanted to provide an isolated example of each type, that is, an example of alpha decay, an example of beta decay, and an example of gamma decay. Which is where the problem lies. Giving an example of alpha or beta decay is easy, just ignore any other possible radiations when you do it, which is the "traditional" method for teaching nuclear decay to Years 9 or 10, or indeed Year 11 chemistry (and yes, physics teachers are probably horrified, and rightly so, IMHO). But, you can't do this for gamma decay unless you want to talk about "excited states".

Which brings us to version 9 of the Australian Curriculum for Year 9 Science which states,

"describing in simple terms how different unstable isotopes decay such as radon-222 releasing an alpha particle, iodine-131 releasing a beta particle and cobalt-60 releasing gamma radiation to form stable atoms"

Alpha decay of radon-222 and beta decay of iodine-131 ... OK, can do.

Gamma decay of cobalt-60 ? Problem! Cobalt-60 decays by emitting a beta particle to produce an excited state nickel-60 atom. Excited state nickel-60 loses energy by emitting high energy gamma ray and relaxing back to a ground-state nickel-60 atom. But, we can't use this as an explanation because the introduction to excited states won't occur 'til, possibly, year 10 (when they do flame tests).

Has the Australian Curriculum been proof-read?

I think not. Further evidence of the writer's (or writers') slipshod approach to "science" is evidenced in this "interesting" extract (also for Year 9)

"investigating how radiocarbon and other dating methods have been used to establish that First Peoples of Australia have been present on the Australian continent for more than 60,000 years"

Problem 1: radiocarbon dating is pretty useless for anything older than about 40,000 years old, so it would be worse than useless for artifacts said to be 60,000 years old. 

Problem 2: where is the SCIENTIFIC evidence that Australia has been inhabited by humans for "more than 60,000 years"? Surely if you are going to make a statement like this, and force SCIENCE teachers to teach it, you need to support the statement, just a link a two, some references, to some SCIENTIFIC studies would be useful. 

So, here's what I think I know ... Mungo man/mungo woman are thought to be about 40,000 years old (give or take a few thousand). Blackened rocks at Moyjil are thought to be about 125,000 years old, but not linked to human habitation (that I'm aware of). The Pilbara petroglyphs have a wide range of dates depending on who provides them, but they also seem to be scientifically dated between 40,000 and 50,000 years. 

My problem is that I'm not an anthropologist, I know a little bit about chemistry (Chemical Sciences), a bit less about geology (sorry, Earth Sciences), even less about physics (AKA physical sciences), and practically nothing about biology (sometimes called a science), and hence I am NOT in a position to either a) know how long Australia has been inhabited for, or

b) to teach anything about this 

... and I suspect most SCIENCE teachers in Australia would fall into the same category.

AC: Australian Curriculum or Australian C_ _ p?

Ruthenium-106 Cloud

In October 2017 the German Federal Office for Radiation Protection detected a radioactive cloud containing ruthenium-106 wafting over Europe. They identified the Southern Ural Mountains in Russia or Kazakhstan as the most likely source of the cloud. In November 2017 Roshydromet, the authority responsible for monitoring radiation in Russia, finally admitted that it had found extremely high levels of ruthenium-106 at two monitoring stations in this region in late September and early October.

Ruthenium is a transition metal element with the chemical symbol Ru and an atomic number of 44.
 Naturally occurring ruthenium has 7 stable isotopes: ⁹⁶Ru, ⁹⁸Ru, ⁹⁹Ru, ¹⁰⁰Ru, ¹⁰¹Ru, ¹⁰²Ru, and, ¹⁰⁴Ru. The abundance of each isotope in naturally occurring ruthenium is given in the table below:

isotope	abundance %
ruthenium-96	5.54
ruthenium-98	1.87
ruthenium-99	12.76
ruthenium-100	12.60
ruthenium-101	17.06
ruthenium-102	31.55
ruthenium-104	18.62

In addition to these naturally occurring stable isotopes, about 30 unstable, or radioactive, isotopes have also been identified. The most stable of these radioisotopes is ruthenium-106 which has a half-life of  359 73.days. It decays by emitting a beta particle to produce rhodium-106:

106	Ru	→	0	e	+	106	Rh
44			-1			45

Ruthenium-106 is produced in a nuclear reactor as a product of the nuclear fission of uranium-235. Ruthenium-106 can be extracted from spent nuclear fuel and then it can be used in medicine to treat eye tumors.

The radioactive cloud wafting across Europe is most likely to be due to a spill of ruthenium-106 rather than a nuclear reactor accident since this would have released other radioisotopes which would have been detected in the cloud. France's nuclear safety agency has estimated the amount of radiation released at the source as between 100 and 300 billion becquerels.
A becquerel (Bq) is the SI unit for measuring radioactivity. It is equivalent to the radioactive decay of 1 nucleus in 1 second.
We can use this to estimate the mass of ruthenium-106 spilled:

ABq

=

mass       atomic weight

x NA x

ln(2) t½

A_Bq = activity in becquerels = 200 x 10⁹ Bq (averaged)
mass = ? grams
atomic weight = 106 g/mol (from the Periodic Table)
N_A = 6 x 10²³ mol^-1 (Avogadro's number)
t_½ =  373.59 days = 373.59 days x 24 hours/day x 60 minutes/hour x 60 seconds/minute = 3.22 x 10⁷ seconds

200 x 109	=	mass       106	x 6 x 1023 x	0.6931 3.22 x 107
200 x 109	=	mass       106	x 6 x 1023 x	2.15 x 10-8
200 x 109	=	mass       106	x 1.29 x 1016
mass	=	200 x 109 x 106 1.29 x 1016
mass	=	1.64 x 10-3 g

If the source of this ruthenium-106 was an accident involving spent fuel rods, then we can calculate the mass of spent fuel involved since 1.9 kg of ruthenium-106 can be extracted from 1 ton (or 1000 kg) of used fuel.
1.9 kg = 1.9 kg x 1000 g/kg  =  1900 g
1900 g of ruthenium-106 can be extracted from 1000 kg (1 000 000 g) of spent nuclear fuel.
1 g of ruthenium-106 can be extracted from 1 000 000 g/1900 g =  526 g of spent fuel
1.64 x 10^-3 g ruthenium-106 would be produced from 1.64 x 10^-3 x 526  = 0.86 g of spent fuel

A typical nuclear power plant produces 20 tons (2 x 10⁷ g) of  used nuclear fuel per year, about 0.6 grams per second!

Reference:
http://www.smh.com.au/world/with-a-radiation-cloud-comes-a-mystery-from-russia-20171123-gzrvtf.html 

Further Reading:
Isotopes 
Atomic Number (number of protons) 
Mass Number (number of nucleons) 
Calculating Relative Atomic Mass (atomic weight)
Nuclear Half-life 


Suggested Study Questions

1.  What does the term "isotope" mean?
2.  Give the atomic number of each of the following species:
   • ruthenium-96
   • ruthenium-98
   • ruthenium-100
   • ruthenium-102
   • ruthenium-104
   • ruthenium-106
3. Give the mass number (or nuclear number) of each of the following species:
   • ruthenium-96
   • ruthenium-98
   • ruthenium-100
   • ruthenium-102
   • ruthenium-104
   • ruthenium-106
4. Determine the number of protons in the nucleus of an atom of each of the following:
   • ruthenium-96
   • ruthenium-98
   • ruthenium-100
   • ruthenium-102
   • ruthenium-104
   • ruthenium-106
5. Determine the number of neutrons in the nucleus of an atom of each of the following:
   • ruthenium-96
   • ruthenium-98
   • ruthenium-100
   • ruthenium-102
   • ruthenium-104
   • ruthenium-106
6. Use the information in the article to calculate the relative atomic mass (atomic weight) of ruthenium.
7. Explain what is meant by the term "unstable isotope".
8. Explain what is meant by the term "beta decay".
9. A number of unstable isotopes of ruthenium undergo beta decay. Write balanced nuclear decay equations for the beta decay of the following ruthenium isotopes:
   • ruthenium-103
   • ruthenium-105
   • ruthenium-106
   • ruthenium-107
   • ruthenium-108
   • ruthenium-109
10. Explain what is meant by nuclear "half-life"?
11. Ruthenium-106 has a half-life of of  359 73.days. Calculate the percentage of ruthenium-106 remaining after:
    • 359.73 days
    • 719.46 days
    • 1079.19 days
    • 3597.3 days
12. If the mass of ruthenium-106 in the cloud over Europe is currently 1.64 x 10^-3 g, calculate the mass of ruthenium-106 remaining in the cloud after:
    • 1 year
    • 2 years
    • 10 years

Uranium Glass

Uranium compounds have been used to colour glass since ancient times. A mosaic found in a Roman villa dated to about 79 AD used yellow glass containing 1% uranium oxide. Between 1880 and the 1920s, uranium glass was quite popular, not only because of its interesting yellow-green colour, but because it fluoresces in ultra-violet light as shown in the image of a vase below.
The image on the left hand side shows the vase under normal daylight, while the image on the right shows the same vase in the dark exposed to UV light.

Why does uranium glass glow green in the dark like this?
Well, it has nothing to do with the radioactivity of uranium isotopes. The green glow does not occur because of changes within the nucleus of uranium atoms, it occurs because of changes in the energy of electrons surrounding the nucleus.
A ground state electron in a uranium atom absorbs the energy of a photon  of ultra-violet light causing the electron to jump to a higher energy level known as the excited state. This new excited state electron configuration is not stable, so, the electron falls back down to to the ground state energy level, which is a lower energy state, by losing energy which it does by emitting a photon of light. Some of the energy of the original photon used to excite an electron is dispersed as molecular vibration and heat, so the energy of the photon emitted when the excited electron falls back to the ground state is less than the energy originally absorbed.
That is: E = hν/λ
where E = energy, h = Planck's constant, ν = speed of light , λ = wavelength of light
If the speed of light is a constant, then E ∝ 1/λ or Eλ = a constant
in other words, the more energy the photon of light has the shorter its wavelength is.
In the case of uranium glass, the absorbed photon of ultra-violet light has a wavelength of about 300 nm, while the emitted photon of green light has a wavelength of about 550 nm.
The wavelength of the emitted photon of light corresponds to the green part of the visible spectrum.
The emission of visible light in this way is known as fluorescence.

Further Reading:
Isotopes
Radioactivity: Properties and Uses
Emission Spectra
Flame Tests

Suggested Study Questions

1. Uranium is found in nature as one of three isotopes, uranium-234, uranium-235 and uranium-238. Explain how atoms of each isotope are:
• the same
• different
2. Atoms of neptunium-234, neptunium-235 and neptunium-238 have been synthesized. Explain the similarities and differences between each of the following pairs of atoms:
   • neptunium-234 and uranium-234
   • neptunium-235 and uranium-235
   • neptunium-238 and uranium-238
3. The value for Planck's constant is 6.626 070 040 x 10^-34 J s and the speed of light is given as 300 000 000 m / s. Calculate the energy of each of the following photons of light:
• ultra-violet light, λ = 300 nm
• green light, λ = 550 nm
4. Using the results of question 3, compare the energy of the photons used to excite uranium atoms and the energy of the photons emitted by uranium atoms and explain the difference.
5. Explain why the same wavelength of light is always emitted when these uranium atoms are exposed to ultra-violet light.
6. Would you expect the uranium glass to fluoresce if it is exposed to infra-red light rather than to ultra-violet light? Explain your answer.
7. Optical brighteners are often used in laundry detergents to make your old, yellowy-looking white clothes look whiter. Typically these compounds absorb ultra-violet light with a wavelength of around 300 nm and emit light with a wavelength of around 450 nm.
   • What colour is the light emitted?
   • What is the energy of the emitted light?
   • Why is the energy of the light emitted not the same as the energy absorbed when the incoming photon hits the "optical brightening compound"?
   • Would you expect a laundry detergent containing "optical brightening compounds" to glow in the dark when exposed to UV light? Explain your answer.

Astatine's Ionization Energy

Astatine is the product of the radioactive decay of some heavier elements and is the rarest naturally occurring element on Earth, only a few grams of astatine is estimated be present in the whole of the Earth's crust at any one time. All of astatine's isotopes are short-lived, with astatine-210 having the longest half-life of all its isotopes, 8.1 hours. As a result, astatine was unknown until 1940, when scientists bombarded bismuth-209 with alpha particles and produced astatine.
Even today we don't know very much about astatine, but estimates about its properties have been made based on its position in the Periodic Table, right under iodine in Group 17 (halogens). The first ionization energy of astatine has been estimated to be between 849.11 and 926.29 kJ/mol (8.8 and 9.6 eV).

The ionization energy, the energy required to remove an electron from the valence shell of an atom, is one of the most important properties that influences the chemical behaviour of an element.

In May 2013 an international team of researchers announced that they had measured the first ionization energy of astatine using laser ionization spectroscopy and found it be be 9.31751 eV (899.02 kJ/mol)

Reference:
Rothe, S. et al. Measurement of the first ionization potential of astatine by laser ionization spectroscopy. Nat. Commun. 4:1835 doi: 10.1038/ncomms2819 (2013).

Further Reading:
http://www.ausetute.com.au/pertable.html

http://www.ausetute.com.au/trendgp7.html 
http://www.ausetute.com.au/trendie.html 
http://www.ausetute.com.au/isotopes.html
http://www.ausetute.com.au/nucledec.html
http://www.ausetute.com.au/halflife.html

Suggested Study Questions:

1. Use the Periodic Table to find the following:
   • astatine's chemical symbol
   • astatine's atomic number
2.  Use the Periodic Table to find the
   • The group astatine belongs to
   • the period astatine belongs to
3. How many valence electrons does an atom of astatine have? Explain your answer.
4. Describe the trend in melting points as you go down astatine's group in the periodic table, then estimate the melting point of astatine.
5. Describe what you think astatine would look like at room temperature and justify your answer on the basis of trends in the periodic table. 
6. How does astatine-207 differ from astatine-210? 
7. Astatine-211 and 2 neutrons are produced when bismuth-209 is bombarded with alpha particles.  Write a nuclear equation for this reaction.
8. Imagine working in a laboratory. You have been given 100 μg of astatine-210 at 9 am for your experiment. Assuming the half-life of astatine is 8 hours, how much astatine-210 would you have left when you leave the lab at 5 pm?
9. The half-life of astatine-219 is about 1 minute. If you had 100 μg of astatine-219 at 9 am, how much astatine-219 would you have 5 minutes later at 9:05 am ?
10. Use the information in the article above to estimate the conversion factor between electronvolts (eV) and kJ/mol. 
11. Why do we not have an accurate measure of how much astatine is found in the Earth's crust?
12. Suggest a way that scientists can estimate the amount of astatine in existence in the Earth's crust.  

Element 118

In 1998, Robert Smolanczuk published some calculations which suggested that it could be possible to produce element 118 by fusing lead with krypton. In 1999, Lawrence Berkeley National Laboratory (LBNL) scientists reported the successful production of element 118 (given the temporary name ununoctium and temporary chemical symbol Uuo) by fusing lead-208 and krypton-86: 


86
36Kr + 208
82Pb → 293
118Uuo + n

Unfortunately, researchers, including LBNL scientists, were unable to duplicate theses results, and in 2002 the director of the laboratory announced that the original claim of the discovery of element 118 (ununoctium) had been based on data that was fabricated by a researcher and was not based on the results of a scientific investigation.

In 2006, researchers at the Joint Institute for Nuclear Research (JINR) and Lawrence Livermore National Laboratory of California announced that they had indirectly detected several nuclei of ununoctium-294, produced by colliding californium-249 atoms and calcium-48 atoms:

249
98Cf + 48
20Ca→ 294
118Uuo + 3n

However, in 2011 the International Union of Pure and Applied Chemistry (IUPAC) said the results did not meet the criteria for the announcement of the discovery of a new element.

Further Reading
Isotopes 
History of the Periodic Table

Suggested Study Questions

1. Give the atomic number for each of the following isotopes:
   • calcium-48
   • krypton-86
   • lead-208 
   • californium-249
   • ununoctium-294
2. Give the mass number for each of the following isotopes:
   • calcium-48
   • krypton-86
   • lead-208 
   • californium-249
   • ununoctium-294
3. Give the number of protons in the nucleus of each of the following isotopes:
   • calcium-48
   • krypton-86
   • lead-208 
   • californium-249
   • ununoctium-294
4. Give the number of neutrons in the nucleus of each of the following isotopes:
   • calcium-48
   • krypton-86
   • lead-208 
   • californium-249
   • ununoctium-294
5. It has been suggested that element 120 with a mass number of 302, and the temporary name unbinilium and temporary symbol Ubn, could be produced by bombarding plutonium-244 with iron-58. Write a possible equation for this reaction.
6. It has also been suggested that element 120 (unbinilium, Ubn) with a mass number of 302 could be produced by fusing uranium-238 and nickel-64. Write a possible equation for this reaction.
7. If unbinilium-302 were to be produced by fusing californium-248 with another atom, what would be the most likely element to use? Justify your answer by writing an equation for the equation.
8. What is the most likely product of the reaction in which californium-249 atoms are fused with titanium-50 atoms? Justify your answer by writing an equation for this reaction.
9. Based on your understanding of the arrangements of elements within the Periodic Table, which group do you think ununoctium would belong to? What would you predict the physical and chemical properties of ununoctium to be?
10. Before 1979, element 118 had been known as eka-emanation or eka-radon because radium "emanation" is an old name for the element radon, so-called because Friedrich Ernst Dorn first noticed that radium compounds emanate, or emit, a radioactive gas, and "eka" was the prefix used by mendeleev when constructing his Periodic Table to denote an unknown element 1 place down in the same Group. Give the current names for the elements which were originally known as:
• eka-caesium
• eka-iodine
• eka-boron
• eka-aluminium
• eka-manganese
• eka-silicon

Bismuth-209

Until recently, bismuth-209 was considered to be a stable isotope, in fact, it was thought to be the heaviest stable isotope, but scientists weren't very happy about the "stable" designation. Measurements of atomic mass and nuclear decay schemes since the 1940's indicated that bismuth-209 should be just a bit too heavy to be truly stable. Then, during the night of March 14-15 2002, a team of scientists from the Institut d’Astrophysique Spatiale d’Orsay (IAS - CNRS, Université Paris XI) stumbled across the alpha decay products of bismuth-209. 

The half-life for the decay of bismuth-209 to  thallium-205 has been reported as 1.9 x 10¹⁹ years. 
In comparison, the estimated age of the universe, starting  from the time of the Big Bang, is just  13.75 x 10⁹ years. Bismuth-209 is therefore a primordial isotope, one that has existed in its current form since before the Earth was formed. 288 primordial isotopes are known, including the 255 stable isotopes plus 33 unstable isotopes with exceptionally long half-lives like bismuth-209.

Reference

http://www.cnrs.fr/cw/en/pres/compress/bismuth.htm 

Further Reading 

Isotopes
Properties & Uses of Radiation
Nuclear Decay
Half-life Calculations

Suggested Study Questions

1. For an atom of bismuth-209, give the
• symbol
• atomic number
• mass number
• number of protons in the nucleus
• number of neutrons in the nucleus
2. For bismuth-209,
• Calculate the ratio of neutrons to protons
• If the nucleus of a heavy metal atom is considered to be stable of the neutron to proton ratio is 1.5:1, would bismuth-209 be predicted to be stable or unstable? Explain your answer.
3. For an atom of thallium-205, give the
• symbol
• atomic number
• mass number
• number of protons in the nucleus
• number of neutrons in the nucleus
4. Give the symbol for an alpha particle.
5. Write an equation for the nuclear decay of bismuth-209 to thalium-205.
6. Current predictions are that the Earth will be demolished during the death of the Sun in about 7 x 10⁹ years. Assuming you had 1 tonne of bismuth-209 today,
   • How much bismuth-209 would remain in 7 x 10⁹ years?
   • How much thallium-205 would have been produced as a result of bismuth-209 decay?
7. Bismuth-209 is produced on earth when lead-209 undergoes beta decay. Write an equation to represent this nuclear reaction.
8. The half-life of lead-209 is about 3.25 hours. If you had isolated 60 grams of lead-209, how long would it take for you to have less than about 1 gram left?