<< Chapter < Page Chapter >> Page >

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.

Got questions? Get instant answers now!

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

Questions & Answers

Propose a force standard different from the example of a stretched spring discussed in the text. Your standard must be capable of producing the same force repeatedly.
Giovani Reply
What is meant by dielectric charge?
It's Reply
what happens to the size of charge if the dielectric is changed?
Brhanu Reply
omega= omega not +alpha t derivation
Provakar Reply
u have to derivate it respected to time ...and as w is the angular velocity uu will relace it with "thita × time""
Abrar
do to be peaceful with any body
Brhanu Reply
the angle subtended at the center of sphere of radius r in steradian is equal to 4 pi how?
Saeed Reply
if for diatonic gas Cv =5R/2 then gamma is equal to 7/5 how?
Saeed
define variable velocity
Ali Reply
displacement in easy way.
Mubashir Reply
binding energy per nucleon
Poonam Reply
why God created humanity
Manuel Reply
Because HE needs someone to dominate the earth (Gen. 1:26)
Olorunfemi
why god made humenity
Ali
Is the object in a conductor or an insulator? Justify your answer. whats the answer to this question? pls need help figure is given above
Jun Reply
ok we can say body is electrically neutral ...conductor this quality is given to most metalls who have free electron in orbital d ...but human doesn't have ...so we re made from insulator or dielectric material ... furthermore, the menirals in our body like k, Fe , cu , zn
Abrar
when we face electric shock these elements work as a conductor that's why we got this shock
Abrar
how do i calculate the pressure on the base of a deposit if the deposit is moving with a linear aceleration
ximena Reply
why electromagnetic induction is not used in room heater ?
Gopi Reply
room?
Abrar
What is position?
Amoah Reply
What is law of gravition
sushil Reply
Practice Key Terms 8

Get the best College physics for ap... course in your pocket!





Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics for ap® courses' conversation and receive update notifications?

Ask