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Radioactivity. Radiation. Radiation : The process of emitting energy in the form of waves or particles. Where does radiation come from?

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Radiation: 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!


What’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.


  • By the end of the 1800s, it was known that certain isotopes emit penetrating rays. Three types of radiation were known:

    • Alpha particles (a)

    • Beta particles (b)

    • Gamma-rays (g)

Where do these particles come from
Where do these particles come from ?

  • These particles generally come from the nuclei of atomic isotopeswhich 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 a

Note: This is theatomic weight, whichis the number ofprotons plus neutrons

Alpha Particles (a)










a (4He)

88 protons

138 neutrons

86 protons

136 neutrons

2 protons

2 neutrons

The alpha-particle(a) is a Helium nucleus. It’s the same as the element Helium, with the electrons stripped off !

Beta particles b
Beta Particles (b)









6 protons

8 neutrons

7 protons

7 neutrons

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 nitrogennucleus. In symbolic notation, the following process occurred:

n  p + e ( + n )

Yes, the same neutrino we saw previously

Gamma particles g
Gamma particles (g)

In much the same way that electrons in atoms can be in an excited state, so can a nucleus.






10 protons

10 neutrons(in excited state)

10 protons

10 neutrons(lowest energy state)


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
Gamma Rays






The gamma from nuclear decayis in the X-ray/ Gamma ray part of the EM spectrum(very energetic!)

Rate of decay
Rate of Decay

  • Beyond 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


% of atomsremaining



  • 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:

1 hour (one lifetime) ?

10,000 (50%)

2 hours (two lifetimes) ?

5,000 (25%)

3 hours (three lifetimes) ?

2,500 (12.5%)

Lifetime t
Lifetime (t)

  • 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 “t” to it.

  • The lifetime of a “free” neutron is 14.7 minutes {t (neutron)=14.7 min.}

  • Let’s use this a bit to become comfortable with it…

Lifetime i
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

N0 = starting number of particlest = 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
Lifetime (II)

Note by slight rearrangement of this formula:

Fraction of particles which did not decay: N / N0 = e-t/t

After 4-5 lifetimes, almost all of the

unstable particles have decayed away!

Lifetime iii
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*, or 2) the “probability” that a given particle will decay.

Lifetime iv
Lifetime (IV)

  • Given a batch of 1 species of particles, some will decay within 1 lifetime (1t), some within 2t, some within 3t, and so on…

  • We CANNOT say “Particle 44 will decay at t =22 min”. You just can’t !

  • All we can say is that:

    • After 1lifetime, 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
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!

Lifetime iv1
Lifetime (IV)

What if we only have 1 particle before us? What can we sayabout it?

Survival Probability =N / N0 = e-t/t

Decay Probability = 1.0 – (Survival Probability)


  • Certain particles are radioactive and undergo decay.

  • Radiation in nuclear decay consists of a, b, and g particles

  • The rate of decay is give by the radioactive decay law:Survival Probability = (N/N0)e-t/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!