Biomedical Engineering Reference
In-Depth Information
EXAMPLE PROBLEM 15.4
Find the energy liberated in the beta decay of
14
6
Cto
1
7
N.
Solution
14
6
C has a mass of 14.003242 amu, and
1
7
N has a mass of 14.003074 amu. Here, the mass differ-
ence between the initial and final states is
D
m
¼
14
:
003242 amu
14
:
003074 amu
¼
0
:
000168 amu
This corresponds to an energy release of
E
¼ð
0
:
000168 amu
Þð
931
:
50 MeV
=
amu
Þ¼
0
:
156 MeV
Only a small number of electrons have this kinetic energy. Most of the emitted electrons have
kinetic energies less than this predicted value. If the daughter nucleus and the electron are not
carrying away this liberated energy, then the requirement that energy is conserved leads one to
ask the question, “What accounts for the missing energy?”
In 1930, Pauli proposed that a third particle must be present to carry away the “missing”
energy and to conserve momentum. Enrico Remi later named this particle the “neutrino”
(little neutral one) because it had to be electrically neutral and have little or no resting mass.
Although it eluded detection for many years, the neutrino (symbol
v
) was finally detected
experimentally in 1950. The neutrino has the following properties:
1.
It has zero electric charge.
2.
It has a resting mass smaller than that of the electron.
3.
It interacts very weakly with matter and is therefore very difficult to detect.
- emitter (
32
P is transformed to
32
S) that
Phosphorus 32 is a typical example of a pure
b
has been used for therapy.
Very often a nucleus that undergoes radioactive decay is left in an excited energy state.
The nucleus can then undergo a second decay to an even lower energy state by emitting
one or more photons. The process is very similar to the emission of light by an atom. An atom
emits radiation to release some extra energy when an electron “jumps” from a state of high
energy to a state of lower energy. Likewise, the nucleus uses essentially the same method
to release any extra energy it may have following a decay or some other nuclear event. In
nuclear de-excitation, the “jumps” that release energy are made by protons or neutrons in
the nucleus as they move from a higher energy level to a lower level. The photons emitted
in such a de-excitation process are called gamma rays and have very high energy relative
to the energy of visible light. Most of the radionuclides undergoing
b
- decay also emit
g
rays,
almost simultaneously. For example, iodine 131 emits several
rays in this process.
The following sequence of events represents a typical situation in which gamma decay
occurs:
b
- and
g
12
0
12
6
C
*
5
B
!
þ
1
e
12
6
C
*
12
!
6
C
þ
g
