Half Life Half-life: time required for half the atoms of a radioactive isotopes of an element to decay. This term is also used to describe decay processes in general. Half-life: The amount of time it takes for half of a given substance to decay is called a half-life. Half-life: See How It Works! click here
Half-lives for various radioisotopes can range from a few to billions of years. Here are some examples:

Radioisotope

Half-life

BPolonium-215

0.0018 seconds

ismuth-212

60.5 seconds

Sodium-24

15 hours

Iodine-131

8.07 days

Cobalt-60

5.26 years

Radium-226

1600 years

Uranium-238

4.5 billion years

Here are some more:

(Chart courtesy of http://www.ndt-ed.org/index_flash.htm) (Second chart courtesy of Charles Sturt University) The half life of an isotope can help us figure out how old an isotope is. It can also aid us in finding out how long it takes for a certain amount of an isotope to decay. For example, Suppose that 10 grams of the isotope Pu-239 was released in the Chernobyl nuclear accident.
How long will it take for the 10 grams to decay to 1 gram.( The half-life of Pu-239 is 24,360 years)
Using the formula: y=Ce^kt
C=initial value
K= Proportionability constant( varies for each Element)
t=time

1=10e^kt-------------------------------------------------------------- 1/10=e^ln(1/2)/24,360 * t
5=10e^k(24,360 yrs.) ---------------------------------------------ln(1/10)=ln(1/2)/24,360 * t
1/2=e^k(24,360 yrs.) ----------------------------------------------t =l n(1/10) * 24,360/ ln(1/2)
ln(1/2)= k (24,360 yrs.)------------------------------------------ t = 80, 922 years
k=ln(1/2)/24,360

This is a chart that represents the decaying process of a substance over a series of years. it shows the substance constantly being cut in half until the substance is depleted. The chart also shows that the decaying process does not happen in a steady pattern but it changes as time goes on. (Duda's notes)

Radium

Ex. The half life of Radium 226 is 1620 years.
So in 1620 years, half of the Radium will have decayed away into some other element (1/2 left).
Then, in another 1620 years, half of the remaining Radium will decay (1/4 left now).
In another 1620 years, half of the remaining Radium will decay (1/8 left now)... etc. Radioactive decay is not a linear event.
(Mel's notes)

It is impossible to describe exactly which unstable nucleus will decay at any given instant. Instead, we can describe how many of a given amount will decay in some time.

Half Life Problem:
A bone sample that originally contained 100 grams of carbon 14 now only contains 12.5 grams of carbon 14. How many years ago was this bone sample part of a living creature?
A. 5730
B. 11460
C. 17190
D. 22920

*
Carbon (C-14) is a radioactive isotope. There is a small percentage of C-14 in our atmosphere due to radiation from space. C-14 bonds with oxygen in the atmosphere to create Carbon Dioxide. The Carbon Dioxide is taken in by plants. In the food chain, animals eat plants. Because of this, eventually all living things aquire a small amount of C-14. When the living creature dies, the radioactive decay begins because no new C-14 is entering the creature. The half-life of C-14 5730 years. Because scientists know what the half-life of C-14 is, they can tell how many half-lives have passed since the creature died. They can then tell how old the creature is. However, if too many half-lives pass, there is a possibility that not enough C-14 exists to date the creature. This means that there are limits to carbon dating. (Mel's notes)

Number of
half-lives
elapsed

Fraction
remaining

Percentage
remaining

0

1/1

100

1

1/2

50

2

1/4

25

3

1/8

12

.5

4

1/16

6

.25

5

1/32

3

.125

6

1/64

1

.563

7

1/128

0

.781

...

...

...

n

1/2n

100(1/2n)

Summary: (from the text book)
radioactive elements decay to other elements when they emit subatomic particles. the radioactive decay rate of an element is measured in terms of a half-life. A half-life is a radioactive isotope is the time needed for half of any given amount of that isotope to decay. for example, radium-226 has a half-life of 1620 years. this means that half of the full amount of radium will decay into other elements in 1620 years. In the following 1620 years half of the remaining radium will decay, leaving a fourth of the original amount. this process of cutting the amount in half until the isotope no longer exists and is completely decayed into another element. the half- life of an substance is different depending on the element. Elements can have a millionth of a second up to 4.5 billion years. How do you measure half-lives? watching a waiting is not a possibility. the half-life of a radioactive substance is related to its of disintegration. The shorter the half-life of an element, the faster the rate of disintegration is and the more active the element is. the half-life can be determined from the rate of disintegration, which can be measured in the lab.

how half- life helps with carbon dating- The half-lives of certain types of radioisotopes are very useful to know. They allow us to determine the ages of very old artifacts. Scientists can use the half-life of Carbon-14 to determine the approximate age of organic objects less than 40,000 years old. By determining how much of the carbon-14 has transmitted, scientist can calculate and estimate the age of a substance. This process is known as Carbon dating. Isotopes with longer half-lives fro example Uranium-238 can be used to date even older objects.

Half-Lives in Medicine__

Radiation therapy is a popular method to treat various forms of cancer. In most cases, ions are used to attack cancer cells. An example would be an ionized form of iodine to treat thyroid cancer. This therapy can be employed either internally (through drinking and more common) or externally. Through the therapy, an indivual becomes radioactive, and has to wait for the half-life to take effect. In most cases, it takes a person two weeks to be around people as they normally would, and in most cases individuals are quarantined until the radiation level diminishes to a "safe" amount. In Positiron Emission Tomography (PET) radioactive isotopes (usually iodine) are also ingested to highlight certain areas of an individual's organs by emitting gamma rays, but these isotopes often have an extremely short half-life, and little to no restrictions are placed on the individual. Half-life is also a term to describe the effects of a medication after it leaves the body, but has nothing to do with radioactive half-life, although the concept is the same. Pictured below is an image of a brain using PET. (Wikipedia and Mr. Duda notes)

Half LifeHalf-life: time required for half the atoms of a radioactive isotopes of an element to decay. This term is also used to describe decay processes in general.Half-life:The amount of time it takes for half of a given substance to decay is called a half-life.Half-life: See How It Works! click hereHalf-lives for various radioisotopes can range from a

fewtobillions of years.Here are some examples:RadioisotopeHalf-lifeHere are some more:

(Chart courtesy of http://www.ndt-ed.org/index_flash.htm) (Second chart courtesy of Charles Sturt University) The half life of an isotope can help us figure out how old an isotope is. It can also aid us in finding out how long it takes for a certain amount of an isotope to decay. For example, Suppose that 10 grams of the isotope Pu-239 was released in the Chernobyl nuclear accident.

How long will it take for the 10 grams to decay to 1 gram.( The half-life of Pu-239 is 24,360 years)

Using the formula: y=Ce^kt

C=initial value

K= Proportionability constant( varies for each Element)

t=time

1=10e^kt-------------------------------------------------------------- 1/10=e^ln(1/2)/24,360 * t

5=10e^k(24,360 yrs.) ---------------------------------------------ln(1/10)=ln(1/2)/24,360 * t

1/2=e^k(24,360 yrs.) ----------------------------------------------t =l n(1/10) * 24,360/ ln(1/2)

ln(1/2)= k (24,360 yrs.)------------------------------------------

t = 80, 922 yearsk=ln(1/2)/24,360

Ex. The half life of Radium 226 is 1620 years.

So in 1620 years, half of the Radium will have decayed away into some other element (1/2 left).

Then, in another 1620 years, half of the remaining Radium will decay (1/4 left now).

In another 1620 years, half of the remaining Radium will decay (1/8 left now)... etc. Radioactive decay is not a linear event.

(Mel's notes)

Half Life Problem:A bone sample that originally contained 100 grams of carbon 14 now only contains 12.5 grams of carbon 14. How many years ago was this bone sample part of a living creature?

A. 5730

B. 11460

C. 17190

D. 22920

*

Carbon (C-14) is a radioactive isotope. There is a small percentage of C-14 in our atmosphere due to radiation from space. C-14 bonds with oxygen in the atmosphere to create Carbon Dioxide. The Carbon Dioxide is taken in by plants. In the food chain, animals eat plants. Because of this, eventually all living things aquire a small amount of C-14. When the living creature dies, the radioactive decay begins because no new C-14 is entering the creature. The half-life of C-14 5730 years. Because scientists know what the half-life of C-14 is, they can tell how many half-lives have passed since the creature died. They can then tell how old the creature is. However, if too many half-lives pass, there is a possibility that not enough C-14 exists to date the creature. This means that there are limits to carbon dating.

(Mel's notes)

half-lives

elapsed

remaining

remaining

nnn)Summary: (from the text book)

radioactive elements decay to other elements when they emit subatomic particles. the radioactive decay rate of an element is measured in terms of a half-life. A half-life is a radioactive isotope is the time needed for half of any given amount of that isotope to decay. for example, radium-226 has a half-life of 1620 years. this means that half of the full amount of radium will decay into other elements in 1620 years. In the following 1620 years half of the remaining radium will decay, leaving a fourth of the original amount. this process of cutting the amount in half until the isotope no longer exists and is completely decayed into another element. the half- life of an substance is different depending on the element. Elements can have a millionth of a second up to 4.5 billion years. How do you measure half-lives? watching a waiting is not a possibility. the half-life of a radioactive substance is related to its of disintegration. The shorter the half-life of an element, the faster the rate of disintegration is and the more active the element is. the half-life can be determined from the rate of disintegration, which can be measured in the lab.

Half-Lives in Medicine__

Radiation therapy is a popular method to treat various forms of cancer. In most cases, ions are used to attack cancer cells. An example would be an ionized form of iodine to treat thyroid cancer. This therapy can be employed either internally (through drinking and more common) or externally. Through the therapy, an indivual becomes radioactive, and has to wait for the half-life to take effect. In most cases, it takes a person two weeks to be around people as they normally would, and in most cases individuals are quarantined until the radiation level diminishes to a "safe" amount. In Positiron Emission Tomography (PET) radioactive isotopes (usually iodine) are also ingested to highlight certain areas of an individual's organs by emitting gamma rays, but these isotopes often have an extremely short half-life, and little to no restrictions are placed on the individual. Half-life is also a term to describe the effects of a medication after it leaves the body, but has nothing to do with radioactive half-life, although the concept is the same. Pictured below is an image of a brain using PET. (Wikipedia and Mr. Duda notes)

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