Nuclear Physics
Nuclear Symbols
Mass number, A
(p+ + no)
235
92
U
Atomic number, Z
(number of p+)
Element symbol
Balancing Nuclear Equations
Areactants
235
+ 1
= 142
U  n
235
92
92
1
0
+
0
=
=
Aproducts
+
91
+ 3(1)
Ba  K r  3 n
142
56
56
Zreactants
=
91
36
+
36
Zproducts
1
0
+ 3(0)
Balancing Nuclear Equations #2
222
226 = 4 + ____
226
88
Ra   
4
2
222
86
Rn
88 = 2 + ___
86
Atomic number 86 is radon, Rn
Balancing Nuclear Equations #3
95
235 + 1 = 139 + 2(1) + ____
U n
235
92
1
0
I 2 n
139
53
1
0
95
39
39
92 + 0 = 53 + 2(0) + ____
Atomic number 39 is yttrium, Y
Y
Alpha Decay
Alpha production ():
an alpha particle is a
helium nucleus
4
2
He
U  He 
238
92
4
2
U 
238
92
4
2
or 
2
4
2
2
234
90
Th
234
90
Th
Alpha decay is limited to heavy, radioactive
nuclei
Alpha
Radiation
Limited to
VERY large
nucleii.
Beta Decay
Beta production (b):
A beta particle is an
electron ejected from
the nucleus
0
1
Th 
234
91
Th 
234
91
234
90
234
90
b
0
1
e or
Pa 
0
1
Pa 
0
1
e
b
Beta emission converts a neutron to a proton
Beta
Radiation
Converts a
neutron into
a proton.
Gamma Ray Production
Gamma ray production (g):
238
4
92 U  2 He

234
90Th

0
20 g
Gamma rays are high energy photons
produced in association with other forms of
decay.
Gamma rays are massless and do not, by
themselves, change the nucleus
Deflection of Decay Particles
attract
Opposite charges_________
each other.
repel
Like charges_________
each other.
Positron Production
Positron emission:
Positrons are the
anti-particle of the
electron
22
Na
11

0
1
e
0
e
1

22
Ne
10
Positron emission converts a proton to a neutron
Electron Capture
Electron capture: (inner-orbital electron
is captured by the nucleus)
201
0
201
80 Hg   1 e  79 Au

0
0g
Electron capture converts a proton to a
neutron
Types of Radiation
Nuclear
Stability
Decay will occur in
such a way as to
return a nucleus to
the band (line) of
stability.
The most stable
nuclide is Iron-56
If Z > 83, the
nuclide is radioactive
A radioactive nucleus reaches a stable state
by a series of steps
A
Decay
Series
Half-life Concept
Sample Half-Lives
STOP
NUCLEAR DECAY KINETICS
Decay Kinetics
Decay occurs by first order kinetics (the
rate of decay is proportional to the number
of nuclides present)
 N 
   kt
ln 
N
 0
ln N  ln No   kt
N0 = number of nuclides
present initially
N = number of nuclides
remaining at time t
k = rate constant
t = elapsed time
Calculating Half-life
ln( 2 ) 0 .693
t1 / 2 

k
k
t1/2 = Half-life (units dependent on rate
constant, k)
Example
Determine the amount of Rn-222 that remains
after 5.0 days if the the half-life is 3.8 days
and you started with 80,000 particles.
No = 80,000 particles
k = 0.182 day-1
N = ?
First find decay constant. k = ln2 / t1/2
Example 2
Determine the activity of Rn-222 that remains
after 7.0 days if the the half-life is 3.8 days
and you started with 285 counts/min.
Ao = 285 counts/min
k = 0.182 day-1
N = ?
First find decay constant. k = ln2 / t1/2
Example 3
Determine the percentage of Rn-222 that remains
after 9.0 days if the the half-life is 3.8 days.
No = ??? particles
k = 0.182 day-1
N = ?
First find decay constant. k = ln2 / t1/2
Nuclear Fission and Fusion
Fusion: Combining two light nuclei to form
a heavier, more stable nucleus.
3
2 He

1
4
1 H  2 He

0
1e
Fission: Splitting a heavy nucleus into two
nuclei with smaller mass numbers.
1
0n

235
142
92 U  56 Ba

91
36 Kr
1
 30 n
Energy and Mass
Nuclear changes occur with small but measurable
losses of mass. The lost mass is called the mass
defect, and is converted to energy according to
Einstein’s equation:
DE = Dmc2
Dm = mass defect
DE = change in energy
c = speed of light
Because c2 is so large, even small amounts of
mass are converted to enormous amount of
energy.
Example
Calculate the mass defect and energy released during this
typical fission reaction.
236
92U
 88
36 Kr
236.04556 g
87.91445 g
265.04556 g
+
144
56 Ba
143.92284 g
+
1
40 n
4 x 1.00867 g
235.87197 g
DE = Dmc2 = .2917359 kg x 3.0 x 108 m/s
DE = 8.752 x 107 J
Fission
Fission Processes
A self-sustaining fission process is called
a chain reaction.
Neutrons
Causing
Event
Fission
subcritical
<1
critical
=1
supercritical
>1
Result
reaction stops
sustained reaction
violent explosion
A Fission Reactor
Fusion