# 11.7 Half-life and activity  (Page 5/15)

 Page 5 / 15

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. 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 ${}^{\text{131}}\text{I}$ , ${}^{\text{90}}\text{Sr}$ , ${}^{\text{137}}\text{Cs}$ , ${}^{\text{239}}\text{Pu}$ , ${}^{\text{238}}\text{U}$ , and ${}^{\text{235}}\text{U}$ . Estimates are that the total amount of radiation released was about 100 million curies.

## What mass of ${}^{\text{137}}\text{Cs}$ Escaped chernobyl?

It is estimated that the Chernobyl disaster released 6.0 MCi of ${}^{\text{137}}\text{Cs}$ into the environment. Calculate the mass of ${}^{\text{137}}\text{Cs}$ 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 $N$ released. Since the activity $R$ is given, and the half-life of ${}^{\text{137}}\text{Cs}$ is found in Appendix B to be 30.2 y, we can use the equation $R=\frac{0\text{.}\text{693}N}{{t}_{1/2}}$ to find $N$ .

Solution

Solving the equation $R=\frac{0\text{.}\text{693}N}{{t}_{1/2}}$ for $N$ gives

$N=\frac{{\text{Rt}}_{1/2}}{\text{0.693}}\text{.}$

Entering the given values yields

$N=\frac{\left(6.0 MCi\right)\left(\text{30}\text{.}2 y\right)}{0\text{.}\text{693}}\text{.}$

Converting curies to becquerels and years to seconds, we get

$\begin{array}{lll}N& =& \frac{\left(6\text{.}0×{\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}\text{Ci}\right)\left(3\text{.}7×{\text{10}}^{\text{10}}\phantom{\rule{0.25em}{0ex}}\text{Bq/Ci}\right)\left(\text{30.2 y}\right)\left(3\text{.}\text{16}×{\text{10}}^{7}\phantom{\rule{0.25em}{0ex}}\text{s/y}\right)}{\text{0.693}}\\ & =& \text{}3\text{.}1×{\text{10}}^{\text{26}}\text{.}\end{array}$

One mole of a nuclide ${}^{A}X$ has a mass of $A$ grams, so that one mole of ${}^{\text{137}}\text{Cs}$ has a mass of 137 g. A mole has $6\text{.}\text{02}×{\text{10}}^{\text{23}}$ nuclei. Thus the mass of ${}^{\text{137}}\text{Cs}$ released was

$\begin{array}{lll}m& =& \left(\frac{\text{137 g}}{\text{6.02}×{\text{10}}^{\text{23}}}\right)\left(3\text{.}1×{\text{10}}^{\text{26}}\right)=\text{70}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{g}\\ & =& \text{}\text{70 kg}\text{.}\end{array}$

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.

Activity $R$ 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 $R=\frac{0\text{.}\text{693}N}{{t}_{1/2}}$ , the activity decreases as the number of radioactive nuclei decreases. The equation for $R$ as a function of time is found by combining the equations $N={N}_{0}{e}^{-\mathrm{\lambda t}}$ and $R=\frac{0\text{.}\text{693}N}{{t}_{1/2}}$ , yielding

#### Questions & Answers

what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
how to synthesize TiO2 nanoparticles by chemical methods
Zubear
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Berger describes sociologists as concerned with
Got questions? Join the online conversation and get instant answers!