Operational
Health
Physics
Training (Moe)
2 - RADIOACTIVITY
SECTION
Earlv
A.
he
found
that
a
that
emitting
quantitative
radiations
are
These
radiations,
atom.
Also,
million
continually
times
emit
Moreover,
By
are
fields.
magnetic
radiation,
Since
magnetic
a
the
be
actually
a helium
charge,
similar
to
particles
the
mass
/3
were
in
of
j3
which
charged,
investigation
nucleus
particle
0.000549
a
were
positively
Further
and
not
is
u).
is
in
standard
are
particle
about
in
will
turn,
be more
there
are
These
were
given
three
the
radiation.
(7)
indicating
be
but
a
and
that
cannot
the
unstable
product
fields,
radiation
of
chemical
These,
gamma
in magnetic
charged
that
deflected
a form
of
in
electro-
light.
deflected
particles,
the
a different
the
two were
that
an
direction
oppositely
was deflected,
the
- two positive
actually
in
a particle
whereas
revealed
(>e
and
(B> ,
the
lost.
materials
end
2.1).
that
nucleus
was shown
Figure
Gamma
is
than
charged.
it
and that
the
new atoms.
the
property
constantly
radiations
to form
can be deflected
It
direction
these
fields,
beta
(a>,
found
released
but
(see
particles.
field
producing
magnetic
types
energy
rates
radiation
charged
magnetic
to
of
of
two
the
also
come from
seemed
radioac-
this
element
is
1896,
experiments
given
radioactive
substances,
alpha
first
atoms
other
use
designations:
than
that
energy
energy,
by
characteristic
to
types
From
the
at
the
distinct
they
intense
more
transform
may
stable.
released
They
that
so
the
the
in
phenomenon
showed
of
exist.
therefore
energy
radiation
property
in
which
earlier
this
and others
emitted
and
called
radioac-
plates
radiation
a year
Curie
by her
a specific
of natural
and photographic
produced
relationships
the
reactions.
The
is
discovery
a penetrating
Madame
investigation
radiation
certain
had
tube.
the
salts
emitted
Roentgen
discharge
with
uranium
uranium
which
Further
credited
with
the
gas
tivity.
is
working
to
with
of
Becquerel
While
similar
PROPERTIES
Historv
Henri
tivity.
AND ITS
/?
the
is
a particle
charges,
electron
was shown
negatively
is
mass number
(e-
the
charged.
it
particle
in
-
one
4)
negative
Operational
Health
Physics
Training (Moe)
-
GAMMA
ALPHA
RADIOACTIVE
SOURCE
Figure
2.1
Radiation
deflection
in a magnetic
field.
The field is
perpendicular
to and directed
into the plane of the
paper.
(R.E.Lapp
/ H.L.Andrews,
NUCLEAR
RADIATION
Reprinted
by
permission
of
PHYSICS,
2/e 1954, 1~73.
Prentice-Hall,
Inc., Englewood
Cliffs, NJ).
Following
naturally
occurring
member,
and
Becquerel's
of
the
a
series
very
2-D);
ends
each
up
as
half
life
the
a
have
neptunium
(Pb)
With
the
atom,
electron
of
particles,
in
number
of
and
isomeric
capture
associated
232n,
the
initial
which
is
a radon
the
parent,
(Rn)
parent
but
- see
and
each
series,
named
was later
has
decay
occurring
241Pu
237Np,
series,
series,
isotope;
An artificially
with
to
236~
and
each
nuclei
three
or first
9 238~
and actinium
properties:
half
that
after
the
produced
by
238U. 1
discovery
a
The
are
common
beginning
in
revealed
uranium
isotope.
series,
radionuclide
bombardment
for
member
lead
existed.
thorium,
certain
(time
studies
chains,
the
gaseous
a stable
longest-lived
stable
chains
has
or
called
These
further
series
series,
are
long
called
neutron
radioactive
these
respectively.
discovery,
with
These
are
the
neutrino
useful
in
the
explanation
1934,
that
additional
radioactivity
decay
transitions).
radioactive
and the
of
/3
modes,
In
decay,
anti-neutrino.
decay.
can be induced
have
emerged
(such
addition,
a number
have
been
These
The neutrino
also
particles
in
a
as
of new
uncovered.
have
and anti-neutrino
been
Operational
Health
Physics
Training (Moe)
2-3
are
almost
carry
massless
away
positron,
are
particles
energy
was
in
In
increased
decays.
discovered,
emitted.
the
(<
Also,
the
as well
addition,
of
of
electron
anti-particle
advent
the
the
to
as radioactive
the
complexity
10m3
number
of
the
decay
of
high
known
mass)
in
energy
which
electron,
which
the
positrons
accelerators
particles
has
and
their
decay
as
4OK >
147Sm
series,
or
decay
by the
emission
mechanisms.
and
Other
naturally
137Re,
etc.,
chains,
have
which
also
been
Radioactive
B.
When
an
2.2.a).
so that
can
be
this
at
a
of
decay
scheme
layout,
arrow
to
right.
An
which
238U
a
AX
Z
and
the
some
to
follow.
the
that
a
the
of
ground
the
product
emission
left;
states
(or
state
higher
(called
of
of
the
positively
decay
is
parent,
234Th
is
the
diagram
shown,
the
a
energy
( accounting
as
emission
of
well
of
the
as
the
difference
the
the
recoil
a will
daughter,
Figure
is
atom
level)
than
the
the
of
bring
the
emission
He
with
the
shown
is
the
in
the
a discrete
energy
parent,
the
is
the
In
is
and
energy
so that
parent
by a
by an arrow to
+ 4He,
emitted
of
indicated
radiation
daughter
masses
not
(see
product).
233u+234m
between
for
scheme
daughter
a
net
number
energy
radiation
the
mass
the
charged
of
the
are
charged
A-4y
z-2
state
a decay
ground
negatively
the
particle
the
position
decay
by 2 and
called
energy
figure,
of
equals
cases,
the
the
In
which
and
long
Z decreases
different
the
example
particle.
energy
of
or decays,
a diagram
vertical
the
is
number
by
the
higher
state
an
shown
In
ground
by
members
a transition,
atomic
diagram,
scale.
shown
undergoes
by 4,
In
vertical
atom
the
This
not
such
found.
particle,
A decreases
are
radionuclides,
Transformations
an
alpha
occurring
level
of
daughter
daughter).
decaying
of
In
nuclide
a y ray
may
Operational
Health
Physics
Training (Moe)
2-4
A
A
X
Z
Y
Y
A
Y
z+1
a) Alpha
b) B’+
Decay
Y Decay
Y
z-1
cl B++
d) EC Decay
Y Decay
e) IT Decay
Figure
2.2
Decay
schemes for various
modes of decay:
aI $ $ y, EC and IT.
Operational
Health
Physics
Training (Moe)
2-5
When the transformation
is by negative
j3 emission,
the atomic
number Z increases by 1, but the mass number A remains the same. The antia 7 ray is emitted
neutrino
i7 carries
off
excess energy.
Often,
following
a
B- decay (see Figure
2.2.b).
Negative
j3 emission
is
likely
to occur if the n/p ratio is too high. The decay is given by
AX + A
zJl+ f3- + Y
Z
in
which
ray (as
number or
the figure.
p-
represents
the electron,
2.2b)
does
shown in Figure
the mass number.
Positron
reaction
is
(/3+
or
It
Oe)
1
'e.
-'
is indicated
emission
The
not
emission
affect
by a vertical
is
shown
in
of
either
straight
Figure
a
gamma
the atomic
line
2.2~.
in
The
AX +A +p++u
z
z- x
in which
case
of
emission.
daughter
that carries
away excess energy. As in the
the neutrino
may be
emitted
after
positron
fidecay,
a -y ray
For positron
emission to occur, the parent mass must exceed the
mass
than
two
electron
masses (2 moc2). An
bY more
competes with
positron
decay is electron
mode, which often
v
is
alternate
capture
(EC), pictured
in Figure
2.2d.
It
should
be noted that some
capture.
Of
diagrams
picture
/3+ decay in the same manner as electron
for positron
emission stated above is not met,
course,
if
the condition
then only electron
capture may occur. For this reaction,
$rloe-tA
z- 1
+u.
The electron
which is captured is most often a K shell electron,
although
X rays which are emitted following
L and M capture
are also possible.
electron
capture
will
be those from element
Y. Positron decay and/or
electron
capture are likely
to occur if the n/p ratio is too low.
Operational
Health
Physics
Training (Moe)
2-6
Sometimes
a
than
rather
ray,
As stated
before,
mass number,
so
The
asterisk
2.2e,
In
emission.
B- in
of
the
the
An
this
The
alternate
mode
(see
and
a number,
not
be
of
atomic
number.
n
prompt
and
If
the
of
by
half
delayed
nuclide
neutron
.I’
where
the
state
of
the
by each
given
mode.
7,
Figure
m stands
is
for
may be
followed
a higher
is
the
which
the
by
energy
fraction
nucleus
the
In
of AX,
gives
of
or
A photon
emission
an excited
number
state.
available.
ground
electrons,
decay
observed
in
This
called
internal
nucleus
then
transfers
ejected
with
a
high
process
mass
number
often
substances
competes
with
CY
-kW + k 1,
Z-Z'
0
original
nuclide
neutrons
are
in
indicated
a
atomic
ratio
emission
orbital
fission,
in
spontaneous
with
has
emission.4
and
same number
k is
an average
varies
fission
B
the
value.
the
the
arrow
marked
in
an excited
itself
will
The
total
mass
and the
shorter
spon-
neutrons,
this
process
Y and W,
of neutrons
with
releases
particles,
energy
Since
two fragments
Z and A seem to have
a vertical
enough
into
The
fission
Since
rays
by simply
so
even
lives.2
-y
Ax splits
emitted.
each
Nuclides
fission
for
fission.
released
taneous
decay
of
+ A-A'
k,
number
are
transition.
is
released
some times
the
spontaneous
above,
decay
AmX,
involves
proceed
the
an excited
as a y
3.2).
The reaction
the
of
of
one of
AX+A'y
z Z'
In
mode
which
in
two paths
energy
an isomeric
the
by
the
emit
affect
is
to
will
called
not
to AY. The branching
z+1
mode
is
is
indicated
level
energy
(D230)
is
state
nucleus
excited
to
Another
the
the
Instead
energy
decay.
that
does
scheme,
alternate
discrete
emission
transitions
conversion.
excited
This
decay
transition
total
an
a particle.
state
this
from
in
this
excited
metastable.
B-
emit
indicates
the
emitted
nucleus
fragments,
complex
mode
is
SF.3
state,
it
may also
is
rare,
and the
Operational
Health
Physics
Training (Moe)
2-7
neutron sources, such as those for
time very
short,
practical
found.
a, B 01: 7, are not readily
Included
with
the diagram
of the decay scheme is other useful
information
about the nature of the process. Sometimes, the complex nature
of the process
does not allow
all of the information
to be displayed.
in Figure
2.3,
is the decay scheme for
24Na, adapted
from
Shown
out some of the data which is supplied for simple
Reference
5, to point
emission
decay schemes.
figure,
In
the
half
life
of 15 h. For
fraction
of transitions
the intensity),
as well
/3 is shown. That is, fi-, is
1
and
the
maximum
energy
24Na
is
indicated
as
a /3-
emitter
a
the two p- groups which are emitted,
the
in which that
p- is emitted
(often
called
as the maximum energy (in MeV) of the emitted
emitted in 99.9% of the transitions
of
this
p
is
1.39
MeV.
The emission
4.123
.;01
4.144
\
MeV
Y2 1.369
MeV
1
;;Mg
Figure
with
2.3
Decay scheme for 24Na.
o.o
(STABLE)
of the
Operational
Health
Physics
Training (Moe)
2-8
/I
produces
24Mg
but
the
stable
24Mg
The
excited
nucleus
radiation.
For
2.754
MeV
small
number
7 is
the
majority
or
to
the
of
decays
1.369
MeV,
ground
state
involving
or
schemes
4.123
if
1.369
p-2
7
are
(O.l%),
is
above
emitted.
emission
two
MeV,
MeV
/I2
by
(99.9%),
by one of
transitions
either
rays,
of y
one of
emitted.
For
only
one
in
diagram
the
1.369
MeV
emitted.
3,5-7,
and
prepared
specifically
the
average
sources
other
8-10.
useful
excerpt,
Figure
isotopes.
atomic
weight
radioactive
A
isotope
which
symbol
are
stable
and
This
Z
that
for
each
at
the
far
atomic
and
*H).
artificially
found
in
nature.
nuclides,
produced.
such as 1 H,
the
number.
is
mass
the
percent
the
The
are
left
in
side
of
the
top
has
of
line
The
second
1 H which
of
line
is
row.
each
the
the
the
indicates
the
in
the
a
radio-
square
gives
in
row are
represent
present
column
as found
space
of
The
row gives
in
spaces
known
column.
element
the
first
of
each
spaces
the
a row are
three
each
that
of
the
White
in
with
nucleus
in
i.e.,
spaces
hydrogen
well
general
shown
an element,
Shaded
at
stable.
The number
mass units)
rectangle
is
lists
vertically
(n)
lH
black
chart
This
point,
horizontally.
space
of
G).
that
increases
diagrams,
radioactive)
filled
Note
than
Other
(or
this
individual
gives
energy.
rather
300 are
at
has been
unstable
row represents
increases
(in
combination
about
element.
of neutrons
atomic
isotopes.
only
which
maximum
form
about
in
the
calculations,
the
(Appendix
and the
that
= A-Z
bordered
stable
abundance.
N
than
tabular
interest
number
heavily
(a
For
of
of
number
nature
Nuclides
Each horizontal
isotopes
total
in
3,
dosimetry
rather
form
concerning
Reference
information
which
He = helium,
number
chemical
the
chart,
2.4.
The
The
of
found
information
internal
data,
of
of
the
hydrogen,
known
Chart
nuclides,
of
in
energy,
source
the
features
nuclides
use
References
in
be
properties.
scheme
2,000
the
for
can
additional
nuclear
decay
is
neutron
with
of useful
nuclides
=
along
transition
Another
over
decay
/3
can be found
the
state,
state,
followed
of
transition
is
excited
returns
immediately
References
the
an
ground
Transformation
H
in
gives
isotopic
element
Operational
Health
Physics
Training (Moe)
2-9
He
4.0026
1.00797
nl
ll.Om
p-O.782
1.008665
0
Figure
hydrogen
is
the
it
atomic
For
symbol
the
present
a
followed
by
occurring
lines
neutral
/3-
life,
modes
7
of
To
N,
a target
to
the
and
for
the
designed
let
the
of
by
line
of
first
the
the
line
half
MeV).
space
of very
the
gives
life.
For
0.0186
gives
the
Additional
'H,
MeV
the
listing
which
is
not
long-lived,
naturally
abundance.
Subsequent
excited
Each
state
Isomers
emissions.
are
nuclear
state
has
own half
shown
its
on the
is
chart
radionuclide.
a radioactive
the
location
nucleus
a
bottom
modes.
bombarded,
easy
case
states.
product
original
decay
the
isomeric
given
allow
(in
long-lived
of
the
the
gives
a
the
is
3H,
energy
second
decay
and energy
square
when
In
called
are
mode,
trace
example,
for
line
maximum
the
as
energies
radionuclides,
These
by a divided
second
and
at
lH.
such
emission.
data
decay
atom
The
emitter
any
The number
nuclides,
number.
certain
possible.
number
the
decay
the
For
is
of
in nature.
radionuclides,
give
nucleus
found
unstable
mass
indicates
It
is
mass
and
lines
N
Excerpt from Chart of Nuclides.
(Knolls Atomic
Power
Laboratory.
Schenectady,
New York. Operated by the
General
Electric Co. for Naval
Reactors, The U. S.
Department
of’ Energy).
2.4
as
2
1
emission.
have
decay,
scheme
in
on the
Chart
an atomic
The product
or
to
Figure
of
2.5
the
number
nucleus
find
a product
may be used.
Nuclides.
For
Z and neutron
will
be found
Operational
Health
Physics
Training (Moe)
2-10
$
a
in
‘He
in
z+2
Pout
z+1
Z
p
2H
in
in
n
oflK;Iw
out
NUCLEUS
3H
in
n
in
+
3H
2H
P
out
out
out
a
3He
out
out
N-2
N-l
z-1
z-2
Figure
on
the
an
a
2.5
chart
at
For
the
c.
Decav
Law
When
one
radioactive
of
atoms
decaying
the
a
one
plots
the
activity
Z-2
N=146,
Chart
N+2
with
in
a
percentage
ratio
curve
tionship.
If
the
straight
line
is
t=O,
obtained
same
obtained.
ratio
is
of
first
second
of
time
the
atoms,
graph
indicates
an exponential
This
indicates
paper
on semilog
that
be found
at
corresponds
and
is
that
For
counting
of
(Figure
number
of
radioactive
atoms
sample.
time
2.6)
If
(t)
versus
or logarithmic
paper
all
example,
the
the
some later
be
so on.
found
pattern.
of
to
can then
The number
at
on linear
is plotted
it
activity
activity
is
will
daughter,
decay
the
238U which
daughter
interval.
called
of
location
and some means
given
interval
time
the
case
product
the
same general
source
the
G, this
numbers
the
time
at
find
In
daughter
chain,
large
follow
decay
the
so the
to
a radioactive
a given
and N-2.
in Appendix
nucleus
deals
which
the
N+l
radioactive
original
has
in
t,
From
substances
one
time
location
and
tracing
considered
assume
the
Z=92
and N=144.
234Th.
N
Location chart for nuclear products. (Knolls Atomic power
Operated
by the
Laboratory,
Schnectady,
New York.
GeneralElectric
Co. for Naval Reactors,the
U&Department
of Energy.)
emitter,
Z=90
Js’
EC
out
(Figure
decay
to
the
rela2.7),
a
is
an
Operational
Health
Physics
Training (Moe)
80
60
3
2
1
5
4
6
TIME UNITS
Figure 2.6
Radioactive
Decay, linear plot.
100
\
\
‘;;
a
z5 10
i=
2
\
\
1
0
1
2
3
4
5
TIME UNITS
Figure 2.7
Radioactive
decay, semllog plot.
6
-
_-- .-_-
----
~__
Operational
Health
Physics
Training (Moe)
2-12
exponential
(logarithmic)
decrease
in
number
the
fraction
of
gration
N
stant
of
do
the
rate
where
is
proportional
to
At
Vto
the
aN
number
the
constant
in
the
decay
get
the
general
of
during
decay
during
number
of
a constant
time.
each
unit
a unit
of
atoms
Although
the
same
of
the
same
N
radioactive
If
of
of
atoms
present
at
expression
present:
any
time
t.
By including
constant
proportionality
and the
increases.
exponential
we take
(also
minus
When the
relationship
for
the
sign
decay
This
is
y=
a
similar
+ bx.
the
logarithmic
the
resulting
N at
t = 0) will
of
initially
atoms
indicates
expression
radioactive
is
we
left
at
time
t from
if
a sample
of N 0
of
each
side
of
this
equation,
slope-intercept
one uses
straight
form
semilog
versus
line
the
paper
time
will
be
on the
of
consider
the
the
linear
scale,
-), and the
data:
Time
a straight
and plots
be No.
Number of Atoms
80,000
29,432
10,824
3,984
1,464
536
200
we get
2.4
the
scale
An an example,
integrated,
decay:
No-Xt.
to
Thus,
a decrease
present.
logarithm
N = In
constant),
2.3
number
the
a con-
becomes
transformation
as time
atoms
disinte-
2.2
the
the
In
The
-J,N 3
rate
is
time,
time.
N = NoewXt
where
fractional
2.1
the
called
is
units
is
,
proportionality,
X,
equal
the
there
is,
disintegrate
present
N -N
' o
that
during
not
AN
-=is
rate
atoms
AN
-=
At
where
decay
atoms
of
process,
(s)
0
60
120
180
240
300
360
intercept
line,
values
i.e.,
of
N on
the
slope
of
(the
value
of
Operational
Health
Physics
Training (Moe)
2-13
Plot
a
curve
for
constant
To
cover
of
on
on the
the
slope
atoms
for
two
times;
log
by
choose
of
the
atoms
This
ratio
(1.353
0.3026
readings
for
is
x
time
The
0.1353.
2.3026
the
in
=
In
= -2.
The
log
for
the
t = 120
the
decay
(this
will
1.353
log
+
of
of
In
this
10-l
=
for
the
difference
value
ratio
of
the
ratio,
of
the
For
ratio
at
ratio
of
the
example,
the
number
earlier
is
ln
number
and divide
chosen.
atoms
the
line.
this
values
of
and plot
corresponding
the
s. Take
number
natural
the
Take
natural
the
paper
be a straight
(-X):
time
to
time
and
will
line
t = 0 and
later
10-l)
-
find
difference
the
the
semilog
and lO,OOO-100,000)
scale
The plot
of
the
at
and determine
three-cycle
logarithmic
scale.
find
paper,
lOOO-10,000
the
linear
linear
Take
paper:
100-1000,
atoms
on
element.
on semilog
To
this
and
radioactive
ranges
of
time
semilog
the
plot
the
number
the
on
In
0.1353
1 . 353
two values
time.
= In
_
ln
10
=
is
120 s. We
now obtain
lnN=lnN,
To
and
the
atom
In
N - In
In
N/No
rapidly
= -Xt;
s);
1.67
s-l
time
x 1O-2
on
linear
as abscissa
decay
will
No = -Xt;
-2 = -X(120
plot
The
- Xt;
in
a radioelement
rather
expressed
is
than
paper:
a
number
of
atoms
as ordinate
(y axis)
X
unit
expresses
of
time.
the
The
probability
larger
the
that
value
of
a
X,
number
more
interested
of
atoms
in
present.
the
decay
rate
The activity
of
a given
of
the
more
= At = XN.
sample
a sample
as:
a
dt
single
decays.
usually
the
Plot
(x axis).
constant
decay
One
= x.
2.5
is
Operational
Health
Physics
Training (Moe)
2-14
In
other
words,
multiplying
N,
constant
the
X of
activity
the
number
the
of
element.
At of
the
sample
atoms
present
can be found
at
any time,
by
by the
decay
Accordingly:
N = NoeeXt;
AN = XNoemXt;
At = AoemXt,
where
A, is
equation
the
1.2
mass m of
2.6
activity
and
(decay
2.5
above,
a radionuclide
the
is
At = XN = p
rate)
of
the
expression
given
sample
for
the
at
t = 0.
activity
Combining
of
a known
by:
N,
2.7
D.
half
Half
Life
The
decay
life
of
required
initial
the
and Mean Life
constant
X is
closely
a radionuclide.
for
the
value.
activity
activity
of
Consider
will
to
The half
life
TG is
a given
nuclide
to
an initial
be equal
related
activity
to A,/2.
From
A,.
our
the
concept
defined
decay
as the
to
one-half
At some time
general
of
the
time
of
t = T%,
relationship,
then,
A, = AoemXt;
IA
2O
1
-=e
-XT%
=Ae
O
-XT%
2
In
1 - In
XT% = In
TG = kiLti
x
2 = -XT,,
2;
0.693,
2.8
x
’
.
.
its
Operational
Health
Physics
Training (Moe)
2-15
substituting
the activity
for
X in equation
2.7
in terms of the half life,
At=
In SI units,
activity
a mole of
an alternate
expression
0.693 m Na
AT%
XmNa=
A
Example:
Find the
s°Co (T% = 5.27 y).
gives
6oCo
(dis/s)
for
2.9
of
a
10-3
kg
(1
g)
sample
of
= 0.06 kg, and
-3
23 molecules
A = 0.693 (10
kg) 6.022~10
mole
= 4 . 19x1013dis/s
t
0.06 >
5.27 y 3.1536~10~~
mole
Y
The actual
length of time any one atom survives
may be anything from 0 to
time,
Suppose we were able to sum up all the
infinite
theoretically.
lifetimes
for
the entire sample of atoms. Now, divide by the total number
of atoms,
and we arrive
at the average lifetime
of an atom. The average,
or mean life,
T is given by:
T1 z-=-ii
x
T%
In 2
2.10
1.443 T,,
Given
the activity
At of a sample, the total
will occur in the sample may be obtained from:
Trans.
= 1.433(4.19x1013~)(5.27
= 1.005x1022.
which
2.11
= AtT = 1.443 Ttit
must be
in which
the time units
above, the total number of transitions
Trans.
number of transitions
consistent.
For
the
would be:
y)(3.1536x107
'
Y'
6oCo
example
Operational
Health
Physics
Training (Moe)
2-16
Each
aspects
radioactive
which
characterize
1)
half
2)
energy
3)
type
The
identification
upon
how
well
have
half
life
of
of
when
is
emission,
one knows
the
types
to pinpoint
the
of
energy
for
the
Activity
The
unit
for
radioactive
the
identity
is
activity
but
To
experienced,
11).
to
the
many
are:
differ
an unknown
of
the
search
radionuclides
energy
of
their
have
greatly.
of
techniques
radionuclide.
material
depend
radionuclides
or combination
1
activity
is
dis/s.
unit
later
defined
two units
are
is
aid
in
SI
activity
This
unit
being
used
however,
this
it
may be easier
for
the
type
of
a radioactive
in
an area,
by the
half
approach
of
will
Sometimes,
radionuclide
of
it
life
may not
to
analyze
be
for
emission.
a
designating
the
curie
decay
rate
trans-
(Ci),
rate
of
of
the
the
1 g of
3.7~10~~
by
(1 Ci = 3.7~10~~
unit,
the
are
as
is
whose
the
transformation
Ci.
small
substance
a radionuclide
replaces
taken
as
related
a rather
prefixes
the
originally
1 Bq = 2.703~10-~~
unit.
Three
normally
Many
but
hand,
identification,
the
rate
becquerel
nuclide
factors.
lives
techniques
or
formation
The
half
of
emissions
A becquerel
The
a given
will
same,
other
of
faster
(Bq).
dis/s.4
the
radionuclides,
becquerel
226Ra,
decay.
Units
SI
historical
three
the
their
of
identification
Also,
E.
but
long-lived
these
On
a number
feasible.
of
of
radionuclide
nearly
greatly.
the
For
a particular
are
for
alone.
decay
pattern
and
can determine
which
of
possible
radioactive
emission,
of
Oftentimes,
be required
own unique
emission,
the
one
energy
its
emission
differs
similar
has
the
of
lives
emissions
atom
shown
whereas
large
in
the
range
Table
2.1
curie
of
Bq)
is
a rather
values
(adapted
that
from
large
may be
Reference
Operational
Health
Physics
Training (Moe)
2-17
Table
Prefix
Symbol
deka
hecto
kilo
mega
&a
tera
peta
da
h
k
M
G
T
P
E
exa
Common
are
the
pCi,
smaller
nCi
case
and
two
emit
of
SI units,
Ci = 3.7~10~~
Bq = 37 kBq
sources
in
of
unit
from
6Oco.
rays
one
a
usually
overestimate
counter
which
counting
a
p-
merely
rate,
1
MBq
6oCo
atom
the
6oCo
p
one
which
transformations
decays,
the
will
example,
a beta
1 MBq of
activity
data,
MBq.
(disinte-
as for
then
experimental
some
the
fi
of
counting
of
source,
converts
in
of
the
decay
in
particle
(j°Co
a
would
sample
scheme
of
account.
activity
+
of
emitted,
If
considering
the
expressed
transformations
case,
y/s.
emitter,
all
the
number
this
into
without
counts/s
If
radiations
from
takes
counts
to
of
2.0~10~
be taken
work
become
conveniently
the
In
calculated
counting
transformation
each
and
must
If
refers
emitted.
#8/s
radionuclide
activity
number
For
are
the
be more
Oftentimes,
the
physics
Bq = 37 mBq
use will
time.
in health
these
= 10m6 Ci = 3.7~10~
to be accurately
counts/s.
terms
10-1
10-z
10-e
10-a
10-e
10-12
10-15
lo-18
encountered
1 PCi
is
106
curie
d
a
Bq = 37 Bq
y
1.0x106
In
the
Factor
m
P
n
P
f
= 10eQ Ci = 3.7~10~
1.0x106
counted.
of
Symbol
C
1 nCi
of
If
deci
centi
milli
micro
nano
pica
femto
atto
= lo-l2
greatly
the
101
102
10s
106
109
1012
1016
1018
1 pCi
per
differ
Prefix
units
definition
grations)
- SI Prefixes
Factor
and $i.
Some laboratory
The
2.1
the
the
0.02
source.
observed
(2.0x106)
this
7
rate
(1 count/dis)
the
the
activity
rays
be
may also
and converts
this
to a
decay
For
and
scheme,
example,
2% of
one
will
consider
a
the
gammas.
In
counting
rate
would
be
counts/s
7
to MBq without
=
regard
1.04x
to
Operational
Health
Physics
Training (Moe)
2-18
the
decay
scheme,
overestimate.
did
not
a
counter
be
2x
double
the
true
In
about
interpreted
Since
with
cts/s
Q
,
contains
emitted
per
7Be,
to
a slight
a counter,
occur.
(1 count/dis).
decay,
in
activity
which
Suppose
Then,
the
would
a serious
such
means
which
a
for
a
a
such
result
be 2 MBq,
underestimate
counter.
1
this
emitter,
would
MBq
could
7Be emits
source
counter
the
is
not
the
counting
a
radioactive
This
would
the
radionuclide
counting
equipment
will
When
the
radionuclide
work,
one must
exercise
F.
Snecific
Activity
The
substance.
from
would
converted
counter
equipment
found
in
MBq,
will
could
about
only
be
give
erroneously
situation
normally
be
since
and thus
there
daughter
one
to
the
usually
the
Nevertheless,
chain,
subject
used,
counted,
rate.
is
may
7 rays
the
the
be
more
can be
source
may
of
associated
activity
if
products
potential
different.
being
than
one Q
also
emit
overestimating
Q
the
activity.
When
before
same source
rays
capture
transformation,
particles.
as 1.04
MBq.
emitter
counted
7
This
an
from
this
out
overestimate
which
electron
proportional
determined
of
the
say
counting
an
source
of
as 0.1
a
of
transformation.
1x105
In
serious
come
activity.
counting,
per
a
cts/s,
case
when
7
all
source
would
one counted
p,
lo6
the
if
the
counted
would
0.1
activity
However,
count
occur
the
It
SI
has
units.
to be its
equation
can
then
specific
2.5,
SP.A.
that
be
allow
is
care
in
A
the
usually
been
shorter
obtain
interpretation
half
life
of
The specific
in
any
activity
as
of
choice
Ci/g
the
physics
counting
of
unit
the
this
estimate.
health
per
emitter,
activity
of
activity
frequently
as the
a proper
calibration
a reasonable
expressed
the
is known,
suitable
as occurs
defined
activity.
now expressed
= XN.
made.
unknown,
is
specific
counting
one to
activity
The
one is
data.
mass
of
a
radioelement
the
greater
can be calculated
as
2.12
is
Operational
Health
Physics
Training (Moe)
2-19
where X is the transformation
constant
and N is now the number of
atoms in one kg of the radioelement.
6oCo has a half life
of 5.27 y.
Calculate
the specific
activity:
SP . A. = XN=0.693i&N
T%
and A = .060 moles
Aa'
0a 693 (1) 6.022~10
5.27 y (3.1536~10~
[SP.A.-4.19x10
To convert
l6 hiI (2.703~10
kg
-lL1 31°
a tabulated
SP.A (Bq/kg)
G.
value
23
= 4.19x1016s~
;)*06
-3 k
g
= 1.13~10~
of SP.A. in Ci/g
Ci/g]
to SI units,
use
= 3.7~10~~ SP.A (Ci/g)
Decay Chains
In
general,
most radioactive
substances
do not decay to form a
stable
nuclide,
that
is to say, the daughter nucleus is also radioactive
and
decays with
its
own characteristic
half
life.
The problem
of
determining
the amount of the daughter
present
at any time depends,
therefore,
upon both half
lives.
The daughter
will
be produced at a
certain
rate from the parent, but will decay with its own rate.
at a given time there are NY parent atoms, with decay
Suppose that
atoms. After
a certain
interval
of
constant
and no daughter
%'
atoms, AN2, is
time,
At,
the increase
in the number of daughter
given
by
AN2 = (decay rate
of parent
- decay rate
The decay rate
of the parent
daughter,
since whenever a parent
The decay rate
of the parent
of daughter)
At.
2.13
the formation
rate of the
is actually
atom decays, it becomes a daughter atom.
is XINl,
where Nl is the number of
Operational
Health
Physics
Training (Moe)
2-20
parent
atoms
present
is
X2N2.
daughter
daughter
atoms
per
AN
-= 2
At
From
is
time
Substituting
one arrives
unit
Similarly,
expression
time
general
the
for
decay
rate
the
rate
of
this
of
the
change
of
becomes
2.14
relationship,
the
number
of parent
atoms
= NyemXlt.
at
any
2.15
into
the
above
expression
and
integrating
the
equation,
at
(e-Xlt-e-X2t).
N2=,2-X1
N2 is
the
number
When
the
parent
daughter,
then
negligible
Then
time.
X2N2.
0
NIXl
where
any
The
XINl-
the
Nl
at
2.16
daughter
half
present
is
eWXlt
at
any
long
compared
the
term
and
with
reduces
atoms
life
y$,
compared
equation
of
2.16
after
a
time.
with
that
of
e-X2t
the
becomes
sufficiently
long
time.
to
2.17
However,
since
Nl
= NieeXlt.
we find
N2 = x 1Nl
x2 -Xl'
A
condition
This
activity
stating
is
state
is
decays
this
is
2.18
thus
reached
called
in
transient
at
the
that
the
same rate
formation
which
the
ratio
equilibrium.
as the
rate
of
N2/Nl
In
parent
daughter
this
activity.
atoms
remains
case,
constant.
the
daughter
Another
equals
way of
the
decay
Operational
Health
Physics
Training (Moe)
2-21
rate
of
the
fractional
daughter
atoms.
decrease
constant
in
the
each
parent
unit
of
time
and
daughter
then,
there
is
activities,
with
and
the
238U
parent
reduces
activity
is
extremely
(TG=4.5x10g
x2-x1
so
-x2,
After
then
Y) f
the
that
long-lived,
a
time,
product
state
is
If
the
is
known
The
X1>X2.
characteristic
The
daughter
VP
case
original
expression
-1,
N2
for
then
approaches
given
zero,
and
the
amount
by
2.20
as secular
has
daughter
rises
half
above
life.
In
equilibrium.
a
shorter
to
this
are
(emXlt -emA2 ’ )+
2.16,
Ni
e-X2t
number
of
life
than
and
decays
no equilibrium
been
present.
equation
half
maximum
have
initially
to
a
case,
relationships
N2e -X2t
of
is
presented
If
there
which
gives
are
for
the
daughter,
with
its
own
reached.
cases
daughter
in
which
atoms,
no
we may
2.21
x2-x1
which
instances,
the
the
2.19
e'X2t
parent
atoms
add a term
in
a
Xl<<X2,e-Xlt
(1 - e-X2t).
sufficient
daughter
E-
yielding
as is
N2 = &~1/~2).
N2
same
to
N2 = A;2N'
This
the
ratio.
When
the
In
number
0
N2
is
one
of
the
is
atoms.
interested
The
At = JVX = N2X2
(AtI2
in
activity
for
daughter
the
cy+1>
activity
can be obtained
this
case,
= N2X2
0
= X2A1
atoms
(e-Xlt-e-X2t)+A2e-X2t
present
of
the
by use
at
t = 0.
sample,
of
rather
equation
In
most
than
2.5,
Operational
Health
Physics
Training (Moe)
2-22
When
be
a
radioactive
extended.
1910.
A
The
H.
Decav
The
decay
be
Reference
Curve
of
the
such
a
of
mixture
portion.
type
only
The
shorter-lived
but
as
decay
beginning.
long-lived
=
0,
of
curve
of
curve
are
the
a
of
activity
initial
the
value
activity
The
from
of
each
half
of
the
member
above
can
Bateman
in
of
a series
line
line.
component.
If
remainder
t
of
the
life
straight
=
activity
the
mixture
addition,
of
at
least
decrease
the
back
new straight
zero
of
time.
gives
The
value
can then
at
of values
along
this
original
curve,
the
components,
at
two components,
will
be determined
then
As before,
the
represent
the
component.
component
the
decay
line.
line
as
the
short-lived
this
initially;
activity
line
of
a straight
mixture.
intercept
on the
only
the
is
as rapidly
to
the
values
contains
the
plot.
the
is
sum of
portion
rate
decay
a series
the
the
the
this
0
lines.
by
straight
straight
represents
give
each
followed
of
in
will
for
from
obtained
component
curvature
values
short-lived
for
to
When
the
curve
presence
final
not
corresponding
represent
the
component,
In
When
represents
can be extrapolated
extrapolated
may
counted.
will
portion
long-lived
at
the
a
radionuclides.
3) a final
by the
whereas
for
curve
portion,
by
curve
activity
the
times.
the
greatly
straight
from
straight
contribute
accounts
this
the
being
from
experimental
paper,
followed
of
a radionuclide
of
longest-lived
total
of
a mixture
the
the
final
corresponding
plot
portion
long-lived
will
by H.
n&
the
explained
sample
activity
subtracted
remainders
the
components,
of
the
the
that
then
is
the
out,
activity,
is
curve
in
component,
initial
fact
1) an initial
decay
This
the
life
half
on semilog
which
products
they
Since
the
the
the
from
plotted
contain:
all
to
of
by the
straight
of
due
t
are
of
initial
outlined
developed
quantity
contributions
products
activities
the
the
portion,
two radioactive
in
identifying
will
This
The
the
were
method
12.
of
values
curved
a
2)
for
can be complicated
activity
the
a Mixture
problem
composite
is present,
relationships
equation
in
curve
a
original
general
can be found
chain
graphically
Operational
Health
Physics
Training (Moe)
2-23
If
three
provided
the
or more
original
Example:
Figure
components
data
the
Using
2.8)
and
are
are
present,
sufficiently
data
determine
in
method
can be extended
accurate.
the
the.
this
table,
half
plot
lives
for
a curve
all
the
on semilog
(see
activities
in
the
sample.
P
1; ZOO
5;788
4,078
3,148
2,516
1,666
1,125
770
531
Plot
one
0
1
2
3
4
6
8
10
12
the
would
data
surmise
final
straight
sects
the
graph:
cps.
This
occurs
two
axis
at
the
these
least
curve
at
4000
cps.
time
at which
The half
natural
curve,
t = 12 h,
1#
= -In
14
16
18
20
22
24
26
28
From
the
shape
two components.
to
The half
the
zero
time.
life
is
finding
This
has
this
gives
ratio
the
ratio
curve
the
line
interdirectly
dropped
to
2000
mathematically
of
by the
value
the
determined
activity
the
of
Extrapolate
can be determined
of
This
cps = 4000;
back
life
log
points.
= ln$
at
the
on the
two
are
t
paper.
of
the
4 h.
points
dividing
t = 0,
0
semilog
there
find
the
between
that
=
from
and
on 3-cycle
portion
t
choosing
GE
370
258
181
127
89
62
44
31
t
of
these
two points,
difference
A. Take
by
in
the
time
points:
cps = 500.
8 = -12
A;
0
x
Z-GIn 8
12
3 In 2 =- In 2 h-l
12
4
But
In
T%=-T-=
Take
the
points
corresponding
2
E(4)
h = 4 h.
on the
extrapolated
points
on the
curve
experimental
and subtract
curve.
Plot
their
values
from
these
differences
Operational
Health
Physics
Training (Moe)
2-24
C CURVE
OBTAINED
8Y SUBTRACTING
APOLATED
CURVE
-LIFE
ACTIVITY
OBTAINED
0
2
Figure
4
6
2.8
8
10
Decay curve
OF THE 2-HOL
EIY SUBTRACTING
12 14 16
Time (Hours)
using example
18
B FROM
20
22
data in text.
A
JR
D FROM
24
26
C
28
Operational
Health
Physics
Training (Moe)
2-25
versus
on
the
the
corresponding
experimental
curve
is
cps,
and
difference,
In
enough
this
again
initial
determined
the
points
corresponding
to
is
the
final
straight
cps.
The
on
4,000
on the
not
is
for
t = 0.
experimental
=
Proceeding
in
value
extrapolated
plotted
curve
a straight
line,
portion
half
extrapolated
the
line
cps,
value
on the
the
curve
=
3,400
cps.
The
this
way,
one
life
it
is
a curved
back
to
t = 0 gives
an
this
activity
as
of
line.
2 h.
this
on
straight
is
is
cps,
t = 0;
curve.
curve
graph
6,000
t = 1 h.
the
for
value
extrapolated
for
draw
points
the
cps,
the
the
plotted
2,000
points
a
component
the
of
from
When
plotted,
is
extrapolating
activity
on
points
case
10,000
t = 1 h,
value
cps,
the
difference,
point
the
2,378
determine
Once
the
Consider
is
The
cps.
for
5,778
curve
4,000
Similarly,
can
times.
is
second
again
and its
half
curve
curved
obtained.
life
are
line
and
The
initial
subtracted
the
from
differences
activity
as determined
from
are
of
the
the
this
graph
is
30 minutes.
REFERENCES
S., SOURCE BOOK ON ATOMIC
Princeton,
NJ (1967).
1.
Glasstone,
Co., Inc.,
2.
Denham,
Plutonium
3.
ICRP
ICRP,
Publication
Pergamon
4.
Knoll,
Sons,
Glenn F., RADIATION
New York,
NY (1979).
5.
Lederer,
John Wiley
6.
Shleien,
B.
RADIOLOGICAL
MD (1984).
7.
Brodsky,
TECTION,
8.
NCRP Report
No.
58,
CEDURES, NCRP, Bethesda,
Health
Physics
D.H.,
Elements,
Health
Phys.
38,
Press,
Considerations
16, 475-487
RADIONUCLIDE
Oxford,
England
C.M. and Shirley,
and Sons, Inc.,
ENERGY,
DETECTION
3rd
ed,
in
(1969).
D. Van Nostrand
Processing
TRANSFORMATIONS,
(1983).
Annals
AND MEASUREMENT,
V.S.,
Editors,
TABLE
New York,
NY (1978).
Trans-
John
OF ISOTOPES,
of
Wiley
7th
the
and
ed,
Editors,
THE HEALTH PHYSICS AND
and
Terpilak,
M.S.,
Nuclear
Lectern
Assoc.,
Inc.,
Olney,
HEALTH
HANDBOOK,
A.B.,
Vol.
1,
Editor,
HANDBOOK OF RADIATION
MEASUREMENT
CRC Press,
West Palm Beach, .FL (1978).
A HANDBOOK OF RADIOACTIVITY
MD (1978).
AND PRO-
MEASUREMENTS
PRO-
Operational
Health
Physics
Training (Moe)
2-26
9.
Kocher,
D.C.,
DOSIMETRY
AND
11026 (1981).
10.
Erdtmann,
G.
Verlag
Chemie,
11.
NCRP Report
MENTS, NCRP,
12.
Skrable,
First
155-157
A HANDBOOK OF DECAY DATA FOR APPLICATION
TO RADIATION
RADIOLOGICAL
ASSESSMENTS,
U.S.
DOE Report
DOE/TIC-
and
Soyka,
W.,
THE GAMMA RAYS OF THE RADIONUCLIDES,
Weinheim,
NY (1979).
No.
82,
Bethesda,
SI UNITS
MD (1985).
K.W.,
et al,
Order
Phenomena
(1974).
IN RADIATION
PROTECTION
A General
Equation
for the
and Suggested
Applications,
AND MEASURE-
Kinetics
Health
of Linear
Phys. 27,
Measurement
PROTECTION,
and ProEd. by A.
BIBLIOGRAPHY
Kathren,
tection,
Brodsky,
R.L.,
Historical
Development
of Radiation
HANDBOOK
OF RADIATION
MEASUREMENT
AND
CRC Press,
West Palm Beach,
FL (1978).
Hendee,
Publishers,
W.R.,
MEDICAL
Chicago,
IL
Cember,
Oxford,
Lapp,
Hall,
RADIATION
(1979).
H.,
INTRODUCTION
England
(1983).
R.E.
Inc.,
Evans,
Daughters,
TO
2nd
PHYSICS,
HEALTH
PHYSICS,
2nd
and Andrews,
H.L.,
NUCLEAR RADIATION
Englewood
Cliffs,
NJ (1972).
R.D.,
Engineers'
Health
Phys. l7,
Guide
229-252
to
the
(1969).
ed,
Year
Book
ed.,
PHYSICS,
Elementary
Pergamon
4th
John
Glasstone,
Nostrand
ENERGY,
3rd
Johns,
Charles
Inc.,
Chapter
5,
Princeton,
H.E.
and
C. Thomas,
Cunningham,
Springfield,
Rees,
D.J.,
HEALTH
Cambridge,
MA (1967).
PHYSICS,
SOURCEBOOK
NJ (1967).
J.R.,
THE
IL (1983).
Massachusetts
Caro,
D.E.,
et
al,
INTRODUCTION
Publishing
Co., Chicago,
IL (1962).
Kathren,
R.L.,
AND SURVEILLANCE,
ON
TO
ATOMIC
PHYSICS
Institute
ATOMIC
Prentice
Behavior
2nd ed,
S.,
OF
Press,
ed,
Friedlander,
G., et al, NUCLEAR AND RADIOCHEMISTRY,
Sons, New York,
NY (1964).
Co.,
Medical
of
Wiley
ed,
RADIOLOGY,
of Technology
AND NUCLEAR
Radon
PHYSICS,
and
D. Van
4th
ed,
Press,
Aldine
RADIOACTIVITY
IN THE ENVIRONMENT:
SOURCES, DISTRIBUTION,
Harwood Academic
Publishers,
New York,
NY (1984).
Operational
Health
Physics
Training (Moe)
2-27
/'
Shapiro,
Cambridge,
Gollnick,
Press,
Hurst,
Sons,
J.,
RADIATION
MA (1981).
PROTECTION,
D.A.,
BASIC
RADIATION
Temple
City,
CA (1983).
G.S.
and
Turner,
New York,
NY (1969).
J.E.,
2nd
ed,
Harvard
University
PROTECTION
TECHNOLOGY,
Pacific
ELEMENTARY
RADIATION
PHYSICS,
Press,
Radiation
Wiley
and
OUESTIONS
2.1
When and by whom was radioactivity
2.2
Name the
2.3
With
what
nucleus
are
2.4
With
what
atomic
particle
2.5
When
an
emitted?
2.6
How are
ba:
2.7
three
Q
the
distinct
an a particle
a p particle
a
what
particle?
b.
what
is
version?
Q particles
2.9
What
is
radioactive
the
2.10
To what
portional?
value
2.11
What
does
schemes?
2.12
Describe
occurring
radiation.
identical?
t9 particles
emitted,
Z numbers
is
of
identical?
how
many
a radioactive
nuclear
atom
particles
affected
are
when:
emitted,
particle
the
How does
the
the mass number?
new
was
nuclear
emission
of
converted
particle
a
7
ray
relationship
between
source
at any particular
the
the
are
is
nuclear
2.8
of naturally
is emitted?
is emitted?
When a p particle
a>
b)
types
particle
A and
discovered?
plot
is
the
symbol
of
radioactive
on linear
(common)
on semilogarithmic
affect
graph
paper.
rate
the
decay
and,
rate
from
atomic
versus
in
the
the
number
atoms present
time t?
radioactive
represent
(lambda)
paper
of
release
results
the number of
time t to the
disintegration
X
that
to
radioactive
time:
atoms
B
conand
in
pro-
decay
a
--.-
.~~-.----.
..
_
Operational
Health
Physics
Training (Moe)
2-28
2.13
How many
4
2.14
2.15
cycles
should
b)
c>
700 to 1300 atoms?
20 to 95 atoms?
300 to 120,000
atoms?
What
is
4
b)
common
natural
What
are
the
base
the
c)
e>
lo2
10-4+
What
are
a>
c>
:-1v .
the
common
2.18
What
decay
2.19
If
will
a
In
the
2.20
a>
b)
c>
logarithms
natural
of
logarithms
of
e3
results
by the
value
is
to one-half
its
when the number of radioactive
decay constant
(A)?
defined
by the time
its original
value?
radioactive
half
life
required
substance
loses half
be 6 hours later?
conversion
its
What
is
tegrations
2.22
Why
their
2.23
What
does
define?
the unit
per unit
of source
of time?
may j? emitters
true value?
the
atoms
for
present
a given
activity
in
(N)
isotope
3 hours,
to
what
formula
what does the symbol
TQ represent?
what does the symbol
X represent?
of what number
is 0.693
the natural
2.21
to plot
100
1O-3
b)
What
value
is multiplied
have
of
b)
d)
2.17
paper
logarithms?
logarithms?
a> 1
2.16
semilogarithmic
activity
activity
appear
of
to
logarithm?
based
have
one kilogram
upon
a higher
of
the
number
becquerel
a radioactive
of
value
disin-
than
substance
Operational
Health
Physics
Training (Moe)
2-29
2.24
What
terms
a>
a
b)
the
identify
radioactive
radioactive
material
material?
resulting
that,
radioactive
2.25
Under
what
condition(s),
atoms
to the parent
atoms
such a state?
2.26
Under
what
conditions
daughter
and parent?
2.27
Under
2.28
upon
decay,
does
remain
the ratio
of the number
of
constant
? What is the name
equilibrium
is
no equilibrium
reached?
Assuming
that
good
plot
on semilogarithmic
data
has been obtained,
paper indicate?
2.29
What
known
to
the
2.30
What
value
two points
the intervening
is
condition
term
data?
is
given
is
on
in
another
material?
secular
what
results
projection
reached
what
does
of
a mathematical
obtained
by taking
natural
a radioactive
decay curve
time?
logarithm
and dividing
daughter
given
to
between
a curved
curve
of
the
that
the
decay
beyond
ratio
ratio
of
by
PROBLEMS
2.1
2.2
Complete
a.
'fiRa+Rn
C.
1;~g-+107?
following
decay
schemes
+ He
+
7
If
the
number
of
radioactive
atoms
disintegrate
in
104
radioactive
constant?
Answer:
2.3
the
If
the
active
minute?
Answer:
- 2x10m3
l4 C+N + /3- + i
6
d)
Au+';%g
atoms
at
minutes,
+ ,8- + L
time
what
t
is
is
the
and 2x
2x106,
approximate
minutes
radioactive
constant
atoms,
approximately
208/min
5
b)
is
how
O.l/day
many
and
there
atoms
will
are 3~10~
disintegrate
radioin 1
Operational
Health
Physics
Training (Moe)
2-30
2.4
From the formula
At = A, emXt, find
the activity
of a sample
at 4:00 P.M. when its activity
was 1000 disintegrations
per minute
1O:OO A.M. The decay constant
X of the sample
is 0.2/day.
Answer:
2.5
2.6
951/min
The half-life
Answer:
at
of
radon
0.1813
In problem
2.5,
will
disintegrate
is
3.8235
days.
What
is
the
decay
constant?
d-l
what
in
percentage
1 day? In
of a freshly
2, 3, 4, 5,
separated
sample
10 and 20 days?
of
radon
Answer:
% of radon
decayed
Time(d)
1
2
3
4
5
10
20
2.7
The activity
Bq (dis/s).
16.6
30.4
41.9
51.6
59.6
83.7
97.3
of 10m7 kg of 230Th is found to be 7.2~10~
What is the half
life
of 230Th?
90
Answer:
2.8
The
the
activity
sample
Answer:
2.9
Carbon-14,
specific
Answer:
8.0~10~
years
of a radioactive
1 hour earlier
if
sample
the half
is 25 Bq. What was the
life
is 25 minutes?
132 Bq
14C,
has
activity
1.65X1014
of
a half
'%C?
Bq/kg
life
of
5730
years.
What
is
the
activity
of
Operational
Health
Physics
Training (Moe)
2-31
2.10
Krypton-88,
88Kr has a half
life
of 2.8 hours
and its daughter
rubidium-88,
88Rb has a half
life
of 18 minutes. If the krypton-88
has decayed
to 5xlOlO atoms over
a period
of several weeks, how
many daughter atoms are present? Hint: use the short form formula since
krypton-88
has a much longer half life compared with the half life of
rubidium-88.
Answer:
2.11
232m
Thorium-232,
has a half
life
of 1.41~10~~
years
and
228Ra has a half
life
of 5.76 years. If 10%
daughter
radium-22i,
are found in a lump of natural
ore, how many atoms
atoms of thorium-232
of radium-228
should
be present?
Hint: thorium-232
has an extremely
long half life when compared with the half life of radium-228.
Answer:
2.12
4.085~10~
atoms.
series have half lives of 6
The first
two members of a radioactive
while
the
third member is stable.
minutes
and 12 minutes respectively,
Starting
with
lo8 atoms of the first
member and none of the second
and third,
plot the number of atoms of the three members as a function
of time. Determine from the graph (or otherwise),
the time at which the
second member reaches its maximum.
Answer:
2.13
6~10~ atoms
12 minutes
A smear obtained
beam was counted
recorded
Time (Minutes)
5
10
15
20
25
30
40
50
60
70
80
100
from
with
a
a
Elapsed
graphite block bombarded by a 50 MeV proton
germanium detector.
The following
data was
Counts Per Minute
8400
7104
6008
5102
4300
3600
2591
1820
1310
932
661
330
Plot
the data as (a) linear plot and as a (b) semilog plot.
the half life.
Can you guess what could be the radionuclide?
Determine
I_
-...... - __.---_ ----_--
-----
-
Operational
Health
Physics
Training (Moe)
2-32
2.14
The
half
life
of
of
238U
is
needed
in the old system of
Answer:
2.15
2973
Plot
b)
Determine
t
the
following
data
the
(min)
0
5
10
15
20
25
30
35
Answer:
4.4683~10~
activity
of
years.
How many
kilograms
3.7~10~~
Bq (this
is 1 Ci
kg
The
data in the
of two radionuclides
a>
238U
is
for
an
units)?
- 9.5
table
represents
on semilog
paper
half
of
lives
the
the
two radionuclides
cpm
t (min)
cnm
60,000
34,000
20,000
12,000
7,500
4,750
3,140
2,062
40
45
50
55
60
65
70
75
1406
953
664
457
323
222
152
111
min
and - 4.5
min
’
.
-
decay
curve
of
graphically.
a mixture