Radioactivity

Radiation

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 radiation
on earth is from the sun (solar) or
from radioactive isotopes of the
elements (terrestrial).

Radiation is going through you at
this very moment!

http://www.atral.com/U238.html

Isotopes

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

238

U.

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 forms
of radiation.

 Let’s look at them in more detail…

Alpha Particles

()

Radium

R

226

88 protons
138 neutrons

Radon

Rn

222

Note: This is the
atomic weight, which
is the number of
protons plus neutrons

86 protons
136 neutrons

+

n

n

p

p







He

)

2 protons
2 neutrons

The

alpha-particle



is a

Helium nucleus

.

It’s the same as the element

Helium

, with the

electrons stripped of

!

Beta Particles ()

Carbon

C

1

6 protons
8 neutrons

Nitrogen

N

1

7 protons
7 neutrons

+

e

-

electron

(beta-particle)

We see that one of the neutrons from the C

1

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.

Neon

Ne

20

10 protons

10 neutrons

(in excited state)

10 protons

10 neutrons

(lowest energy state)

+

gamma

Neon

Ne

20

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

Neon

Ne

20

+

The gamma from nuclear decay

is in the X-ray/ Gamma ray

part of the EM spectrum

(very energetic!)

Neon

Ne

20

How do these particles

differ ?

Particle

Mass*

(MeV/c

2

)

Charge

Gamma

()

0

0

Beta ()

~0.5

-1

Alpha ()

~3752

+2

* m = E / c

2

* m = E / c

2

Rate of Decay

Beyond knowing the types of particles which are emitted
when an isotope decays, we also are interested in

how frequently

one of the atoms emits this radiation.

 A very important point here is that we

cannot predict when a

particular 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 to

quantify

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 atoms

remaining

Lifetime ()

 The “lifetime” of a particle is an alternate definition of
the rate of decay, one which we prefer.

 It is just another way of expressing how fast the substance
decays..

 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 of

the

rate of decay

, one which we prefer.

 It is just another way of expressing how fast the substance
decays..

 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 1.7 minutes.

 If I had 1000 free neutrons in a box, after 1.7
minutes some number of them will have decayed.

 The

number remaining

after some time is given by the

radioactive decay law

/

0

t

N N e

t

-

=

/

0

t

N N e

t

-

=

N

0

= starting

number of
particles



= particle’s

lifetime

This is the “exponential”. It’s
value is 2.718, and is a very useful
number. Can you find it on your
calculator?

Lifetime (II)

/

0

t

N N e

t

-

=

Note by slight rearrangement of this formula:

Fraction

of particles which

did not decay

:

N / N

0

=

e

-t/



#

lifetim

es

Tim

e

(min

)

Fraction

of

remainin

g

neutrons

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.0

0.60

0.80

1.00

1.20

0

2



6

8

10

Lifetimes

F

ra

ct

io

n

S

u

rv

iv

ed

0.00

0.20

0.0

0.60

0.80

1.00

1.20

0

2



6

8

10

Lifetimes

F

ra

ct

io

n

S

u

rv

iv

ed

After -5 lifetimes, almost all of the
unstable particles have decayed away!

After -5 lifetimes, almost all of the
unstable particles have decayed away!

Lifetime (III)

 Not all particles have the same lifetime.

 Uranium-238 has a lifetime of about 6 billion
(6x10

9

) years !

 Some subatomic particles have lifetimes that are
less than 1x10

-12

sec !

 Given a batch of unstable particles, we cannot
say 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.

 Not all particles have the same lifetime.

 Uranium-238 has a lifetime of about

6 billion

(6x10

9

) years

!

 Some

subatomic particles

have lifetimes that are

less than

1x10

-12

sec

!

 Given a batch of unstable particles, we

cannot

say 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)

 Given a batch of 1 species of particles, some will decay
within 1 lifetime (1, some within 2, some within 3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

1

lifetime

, there will be

(37%)

remaining

 After

2 lifetimes

, there will be

(1%)

remaining

 After

3 lifetimes

, there will be

(5%)

remaining

 After

 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 lifetimes
are typically only a small fraction of a second!

 If the lifetime is long (like

238

U) 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 lifetimes
are typically only a small fraction of a second!

 If the lifetime is long (like

238

U) it will hang around

for a very long time!

Lifetime (IV)

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

Survival Probability =

N / N

0

= 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/N

0

)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/N

0

)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!