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Radioactivity
Radioactivity
RadiationRadiation: The process of emitting energy in the form of waves or particles.
Where does radiation come from?Radiation is generally produced when particles interact or decay.
A large contribution of the radiationon earth is from the sun (solar) or from radioactive isotopes of the elements (terrestrial).
Radiation is going through you atthis very moment!
http://www.atral.com/U238.html
IsotopesWhat’s an isotope?
Two or more varieties of an element having the same number of protons but different number of neutrons. Certain isotopes are “unstable” and decay to lighter isotopes or elements.
Deuterium and tritium are isotopes of hydrogen. In addition to the 1 proton, they have 1 and 2 additional neutrons in the nucleus respectively*.
Another prime example is Uranium 238, or just 238U.
Radioactivity
By the end of the 1800s, it was known that certain isotopes emit penetrating rays. Three types of radiation were known:
1) Alpha particles ()
2) Beta particles ()
3) Gamma-rays ()
By the end of the 1800s, it was known that certain isotopes emit penetrating rays. Three types of radiation were known:
1) Alpha particles ()
2) Beta particles ()
3) Gamma-rays ()
Where do these particles come from ?
These particles generally come from the nuclei of atomic isotopes which are not stable.
The decay chain of Uranium produces all three of these formsof radiation.
Let’s look at them in more detail…
Alpha Particles ()
Radium
R226
88 protons138 neutrons
Radon
Rn222
Note: This is theatomic weight, whichis the number ofprotons plus neutrons
86 protons136 neutrons
+ nnp
p
He)
2 protons2 neutrons
The alpha-particle is a Helium nucleus.
It’s the same as the element Helium, with the electrons stripped off !
Beta Particles ()
CarbonC14
6 protons8 neutrons
NitrogenN14
7 protons7 neutrons
+ e-
electron(beta-particle)
We see that one of the neutrons from the C14 nucleus “converted” into a proton, and an electron was ejected. The remaining nucleus contains 7p and 7n, which is a nitrogen nucleus. In symbolic notation, the following process occurred:
n p + e ( + Yes, the same neutrino we saw
previously
Gamma particles ()In much the same way that electrons in atoms can be in an excited state, so can a nucleus.
NeonNe20
10 protons10 neutrons
(in excited state)
10 protons10 neutrons
(lowest energy state)
+
gamma
NeonNe20
A gamma is a high energy light particle.
It is NOT visible by your naked eye because it is not in the visible part of the EM spectrum.
A gamma is a high energy light particle.
It is NOT visible by your naked eye because it is not in the visible part of the EM spectrum.
Gamma Rays
NeonNe20 +
The gamma from nuclear decayis in the X-ray/ Gamma ray
part of the EM spectrum(very energetic!)
NeonNe20
How do these particles differ ?
ParticleMass*
(MeV/c2)Charge
Gamma () 0 0
Beta () ~0.5 -1
Alpha () ~3752 +2
* m = E / c2* m = E / c2
Rate of DecayBeyond knowing the types of particles which are emittedwhen an isotope decays, we also are interested in how frequentlyone of the atoms emits this radiation.
A very important point here is that we cannot predict when aparticular entity will decay.
We do know though, that if we had a large sample of a radioactive substance, some number will decay after a given amount of time.
Some radioactive substances have a very high “rate of decay”,while others have a very low decay rate.
To differentiate different radioactive substances, we look toquantify this idea of “decay rate”
Half-Life The “half-life” (h) is the time it takes for half the atoms of a radioactive substance to decay.
For example, suppose we had 20,000 atoms of a radioactive substance. If the half-life is 1 hour, how many atoms of that substance would be left after:
10,000 (50%)
5,000 (25%)
2,500 (12.5%)
1 hour (one lifetime) ?
2 hours (two lifetimes) ?
3 hours (three lifetimes) ?
Time #atoms
remaining% of atomsremaining
Lifetime () The “lifetime” of a particle is an alternate definition ofthe rate of decay, one which we prefer.
It is just another way of expressing how fast the substancedecays..
It is simply: 1.44 x h, and one often associates the letter “” to it.
The lifetime of a “free” neutron is 14.7 minutes {neutron=14.7 min.}
Let’s use this a bit to become comfortable with it…
The “lifetime” of a particle is an alternate definition ofthe rate of decay, one which we prefer.
It is just another way of expressing how fast the substancedecays..
It is simply: 1.44 x h, and one often associates the letter “” to it.
The lifetime of a “free” neutron is 14.7 minutes {neutron=14.7 min.}
Let’s use this a bit to become comfortable with it…
Lifetime (I)
The lifetime of a free neutron is 14.7 minutes.
If I had 1000 free neutrons in a box, after 14.7 minutes some number of them will have decayed.
The number remaining after some time is given by the radioactive decay law
/0
tN N e /0
tN N e N0 = starting number of particles = particle’s lifetime
This is the “exponential”. It’s value is 2.718, and is a very usefulnumber. Can you find it on yourcalculator?
Lifetime (II)/
0tN N e Note by slight rearrangement of this formula:
Fraction of particles which did not decay: N / N0 = e-t/
# lifetimes
Time
(min)
Fraction of remainingneutrons
0 0 1.0
1 14.7 0.368
2 29.4 0.135
3 44.1 0.050
4 58.8 0.018
5 73.5 0.007
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0 2 4 6 8 10
Lifetimes
Fra
cti
on
Su
rviv
ed
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0 2 4 6 8 10
Lifetimes
Fra
cti
on
Su
rviv
ed
After 4-5 lifetimes, almost all of theunstable particles have decayed away!After 4-5 lifetimes, almost all of theunstable particles have decayed away!
Lifetime (III) Not all particles have the same lifetime.
Uranium-238 has a lifetime of about 6 billion (6x109) years !
Some subatomic particles have lifetimes that are less than 1x10-12 sec !
Given a batch of unstable particles, we cannotsay which one will decay.
The process of decay is statistical. That is, we can only talk about either,
1) the lifetime of a radioactive substance*, or2) the “probability” that a given particle will decay.
Not all particles have the same lifetime.
Uranium-238 has a lifetime of about 6 billion (6x109) years !
Some subatomic particles have lifetimes that are less than 1x10-12 sec !
Given a batch of unstable particles, we cannotsay which one will decay.
The process of decay is statistical. That is, we can only talk about either,
1) the lifetime of a radioactive substance*, or2) the “probability” that a given particle will decay.
Lifetime (IV) Given a batch of 1 species of particles, some will decay within 1 lifetime (1, some within 2, some within 3and so on…
We CANNOT say “Particle 44 will decay at t =22 min”. You just can’t !
All we can say is that: After 1 lifetime, there will be (37%) remaining After 2 lifetimes, there will be (14%) remaining After 3 lifetimes, there will be (5%) remaining After 4 lifetimes, there will be (2%) remaining, etc
Lifetime (V)
If the particle’s lifetime is very short, the particles decay away very quickly.
When we get to subatomic particles, the lifetimesare typically only a small fraction of a second!
If the lifetime is long (like 238U) it will hang around for a very long time!
If the particle’s lifetime is very short, the particles decay away very quickly.
When we get to subatomic particles, the lifetimesare typically only a small fraction of a second!
If the lifetime is long (like 238U) it will hang around for a very long time!
Lifetime (IV)What if we only have 1 particle before us? What can we sayabout it?
Survival Probability = N / N0 = e-t/
Decay Probability = 1.0 – (Survival Probability)
# lifetimes Survival Probability
(percent)
Decay Probability = 1.0 – Survival Probability
(Percent)
1 37% 63%
2 14% 86%
3 5% 95%
4 2% 98%
5 0.7% 99.3%
Summary Certain particles are radioactive and undergo decay.
Radiation in nuclear decay consists of , , and particles
The rate of decay is give by the radioactive decay law:
Survival Probability = (N/N0)e-t/
After 5 lifetimes more than 99% of the initial particles have decayed away.
Some elements have lifetimes ~billions of years.
Subatomic particles usually have lifetimes which are fractions of a second… We’ll come back to this!
Certain particles are radioactive and undergo decay.
Radiation in nuclear decay consists of , , and particles
The rate of decay is give by the radioactive decay law:
Survival Probability = (N/N0)e-t/
After 5 lifetimes more than 99% of the initial particles have decayed away.
Some elements have lifetimes ~billions of years.
Subatomic particles usually have lifetimes which are fractions of a second… We’ll come back to this!
