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R = R 0 e λt , size 12{R=R rSub { size 8{0} } e rSup { size 8{ - λt} } } {}

where R 0 size 12{R rSub { size 8{0} } } {} is the activity at t = 0 size 12{t=0} {} . This equation shows exponential decay of radioactive nuclei. For example, if a source originally has a 1.00-mCi activity, it declines to 0.500 mCi in one half-life, to 0.250 mCi in two half-lives, to 0.125 mCi in three half-lives, and so on. For times other than whole half-lives, the equation R = R 0 e λt size 12{R=R rSub { size 8{0} } e rSup { size 8{ - λt} } } {} must be used to find R size 12{R} {} .

Section summary

  • Half-life t 1 / 2 size 12{t rSub { size 8{1/2} } } {} is the time in which there is a 50% chance that a nucleus will decay. The number of nuclei N size 12{N} {} as a function of time is
    N = N 0 e λt , size 12{N=N rSub { size 8{0} } e rSup { size 8{ - λt} } } {}
    where N 0 size 12{N rSub { size 8{0} } } {} is the number present at t = 0 size 12{t=0} {} , and λ size 12{λ} {} is the decay constant, related to the half-life by
    λ = 0 . 693 t 1 / 2 . size 12{λ= { {0 "." "693"} over {t rSub { size 8{1/2} } } } } {}
  • One of the applications of radioactive decay is radioactive dating, in which the age of a material is determined by the amount of radioactive decay that occurs. The rate of decay is called the activity R size 12{R} {} :
    R = Δ N Δ t . size 12{R= { {ΔN} over {Δt} } } {}
  • The SI unit for R size 12{R} {} is the becquerel (Bq), defined by
    1 Bq = 1 decay/s. size 12{1" Bq"="1 decay/s"} {}
  • R size 12{R} {} is also expressed in terms of curies (Ci), where
    1 Ci = 3 . 70 × 10 10 Bq. size 12{1" Ci"=3 "." "70" times "10" rSup { size 8{"10"} } " Bq"} {}
  • The activity R size 12{R} {} of a source is related to N size 12{N} {} and t 1 / 2 size 12{t rSub { size 8{1/2} } } {} by
    R = 0 . 693 N t 1 / 2 . size 12{R= { {0 "." "693"N} over {t rSub { size 8{1/2} } } } } {}
  • Since N size 12{N} {} has an exponential behavior as in the equation N = N 0 e λt size 12{N=N rSub { size 8{0} } e rSup { size 8{ - λt} } } {} , the activity also has an exponential behavior, given by
    R = R 0 e λt , size 12{R=R rSub { size 8{0} } e rSup { size 8{ - λt} } } {}
    where R 0 size 12{R rSub { size 8{0} } } {} is the activity at t = 0 size 12{t=0} {} .

Conceptual questions

In a 3 × 10 9 size 12{3 times "10" rSup { size 8{9} } } {} -year-old rock that originally contained some 238 U , which has a half-life of 4.5 × 10 9 years, we expect to find some 238 U remaining in it. Why are 226 Ra , 222 Rn , and 210 Po also found in such a rock, even though they have much shorter half-lives (1600 years, 3.8 days, and 138 days, respectively)?

Does the number of radioactive nuclei in a sample decrease to exactly half its original value in one half-life? Explain in terms of the statistical nature of radioactive decay.

Radioactivity depends on the nucleus and not the atom or its chemical state. Why, then, is one kilogram of uranium more radioactive than one kilogram of uranium hexafluoride?

Explain how a bound system can have less mass than its components. Why is this not observed classically, say for a building made of bricks?

Spontaneous radioactive decay occurs only when the decay products have less mass than the parent, and it tends to produce a daughter that is more stable than the parent. Explain how this is related to the fact that more tightly bound nuclei are more stable. (Consider the binding energy per nucleon.)

To obtain the most precise value of BE from the equation BE= ZM 1 H + Nm n c 2 m A X c 2 size 12{"BE=" left lbrace left [ ital "ZM" left ("" lSup { size 8{1} } H right )+ ital "Nm" rSub { size 8{n} } right ]-m left ("" lSup { size 8{A} } X right ) right rbrace c rSup { size 8{2} } } {} , we should take into account the binding energy of the electrons in the neutral atoms. Will doing this produce a larger or smaller value for BE? Why is this effect usually negligible?

How does the finite range of the nuclear force relate to the fact that BE / A size 12{ {"BE"} slash {A} } {} is greatest for A size 12{A} {} near 60?


Data from the appendices and the periodic table may be needed for these problems.

An old campfire is uncovered during an archaeological dig. Its charcoal is found to contain less than 1/1000 the normal amount of 14 C size 12{"" lSup { size 8{"14"} } C} {} . Estimate the minimum age of the charcoal, noting that 2 10 = 1024 size 12{2 rSup { size 8{"10"} } ="1024"} {} .

57,300 y

A 60 Co size 12{"" lSup { size 8{"60"} } "Co"} {} source is labeled 4.00 mCi, but its present activity is found to be 1 . 85 × 10 7 size 12{1 "." "85" times "10" rSup { size 8{7} } } {} Bq. (a) What is the present activity in mCi? (b) How long ago did it actually have a 4.00-mCi activity?

Questions & Answers

How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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Source:  OpenStax, Concepts of physics. OpenStax CNX. Aug 25, 2015 Download for free at https://legacy.cnx.org/content/col11738/1.5
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