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Human-made (or artificial) radioactivity has been produced for decades and has many uses. Some of these include medical therapy for cancer, medical imaging and diagnostics, and food preservation by irradiation. Many applications as well as the biological effects of radiation are explored in Medical Applications of Nuclear Physics , but it is clear that radiation is hazardous. A number of tragic examples of this exist, one of the most disastrous being the meltdown and fire at the Chernobyl reactor complex in the Ukraine (see [link] ). Several radioactive isotopes were released in huge quantities, contaminating many thousands of square kilometers and directly affecting hundreds of thousands of people. The most significant releases were of 131 I , 90 Sr , 137 Cs , 239 Pu , 238 U , and 235 U . Estimates are that the total amount of radiation released was about 100 million curies.

Human and medical applications

A person holding a hand held radiation detector near the Chernobyl reactor.
The Chernobyl reactor. More than 100 people died soon after its meltdown, and there will be thousands of deaths from radiation-induced cancer in the future. While the accident was due to a series of human errors, the cleanup efforts were heroic. Most of the immediate fatalities were firefighters and reactor personnel. (credit: Elena Filatova)

What mass of 137 Cs Escaped chernobyl?

It is estimated that the Chernobyl disaster released 6.0 MCi of 137 Cs into the environment. Calculate the mass of 137 Cs released.

Strategy

We can calculate the mass released using Avogadro’s number and the concept of a mole if we can first find the number of nuclei N size 12{N} {} released. Since the activity R size 12{R} {} is given, and the half-life of 137 Cs size 12{"" lSup { size 8{"137"} } "Cs"} {} is found in Appendix B to be 30.2 y, we can use the equation R = 0 . 693 N t 1 / 2 size 12{R= { {0 "." "693"N} over {t rSub { size 8{1/2} } } } } {} to find N size 12{N} {} .

Solution

Solving the equation R = 0 . 693 N t 1 / 2 size 12{R= { {0 "." "693"N} over {t rSub { size 8{1/2} } } } } {} for N size 12{N} {} gives

N = Rt 1/2 0.693 . size 12{N= { { ital "Rt""" lSub { size 8{1/2} } } over {0 "." "693"} } } {}

Entering the given values yields

N = ( 6.0 MCi ) ( 30 . 2 y ) 0 . 693 . size 12{N= { { \( 6 "." 0" MCi" \) \( "30" "." 2" y" \) } over {0 "." "693"} } } {}

Converting curies to becquerels and years to seconds, we get

N = ( 6 . 0 × 10 6 Ci ) ( 3 . 7 × 10 10 Bq/Ci ) ( 30.2 y ) ( 3 . 16 × 10 7 s/y ) 0.693 = 3 . 1 × 10 26 . alignl { stack { size 12{N= { { \( 6 "." 0´"10" rSup { size 8{6} } " Ci" \) \( 3 "." 7´"10" rSup { size 8{"10"} } " Bq/Ci" \) \( "30" "." 2" y" \) \( 3 "." "16"´"10" rSup { size 8{7} } " s/y" \) } over {0 "." "693"} } } {} #" "=3 "." 1´"10" rSup { size 8{"26"} } "." {} } } {}

One mole of a nuclide A X size 12{"" lSup { size 8{A} } X} {} has a mass of A size 12{A} {} grams, so that one mole of 137 Cs size 12{"" lSup { size 8{"137"} } "Cs"} {} has a mass of 137 g. A mole has 6 . 02 × 10 23 size 12{6 "." "02 " times "10" rSup { size 8{"23"} } } {} nuclei. Thus the mass of 137 Cs size 12{"" lSup { size 8{"137"} } "Cs"} {} released was

m = 137 g 6.02 × 10 23 ( 3 . 1 × 10 26 ) = 70 × 10 3 g = 70 kg . alignl { stack { size 12{m= left ( { {"137"" g"} over {6 "." "02 "´"10" rSup { size 8{"23"} } } } right ) \( 3 "." 1´"10" rSup { size 8{"26"} } \) ="70"´"10" rSup { size 8{3} } " g"} {} #" "="70 kg" "." {} } } {}

Discussion

While 70 kg of material may not be a very large mass compared to the amount of fuel in a power plant, it is extremely radioactive, since it only has a 30-year half-life. Six megacuries (6.0 MCi) is an extraordinary amount of activity but is only a fraction of what is produced in nuclear reactors. Similar amounts of the other isotopes were also released at Chernobyl. Although the chances of such a disaster may have seemed small, the consequences were extremely severe, requiring greater caution than was used. More will be said about safe reactor design in the next chapter, but it should be noted that Western reactors have a fundamentally safer design.

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Activity R size 12{R} {} decreases in time, going to half its original value in one half-life, then to one-fourth its original value in the next half-life, and so on. Since R = 0 . 693 N t 1 / 2 size 12{R= { {0 "." "693"N} over {t rSub { size 8{1/2} } } } } {} , the activity decreases as the number of radioactive nuclei decreases. The equation for R size 12{R} {} as a function of time is found by combining the equations N = N 0 e λt size 12{N=N rSub { size 8{0} } e rSup { size 8{ - λt} } } {} and R = 0 . 693 N t 1 / 2 size 12{R= { {0 "." "693"N} over {t rSub { size 8{1/2} } } } } {} , yielding

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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