The Nucleus
345
235
238
( )
( )
N
t
N
t
≈ exp [– t (1/τ 235 – 1/τ 238 )]
(9.87)
Using the observed value of about 1/140 for the relative abundance,
t ≈
235 238
238
235
–
τ τ
τ
τ
ln 140
(9.88)
Since τ 235 ≈ 1.02 × 10
9
years and τ 238 ≈ 6.51 × 10
9
years, the age of the
elements is
t ≈ 5.98 × 10
9
years
(9.89)
This is in reasonable agreement with the age determined from the abundances
of other nuclei. It is also of the same order as the age of the universe deduced
from the rate of expansion of the universe (see Sec. 11.5), and hence is an
important element in the understanding of the universe.
9.6 NUCLEAR REACTIONS
The properties of a nucleus can be studied by bombarding it with energetic
particles, and analysing the consequences of the collisions. If the collision leads
to a nuclear interaction, it gives what is known as a nuclear reaction.
Usually, the projectile is a light particle, it may be a neutron, a proton, a
deuteron, an alpha particle or a photon (recently there has been considerable
interest in heavy ions as projectiles). A typical collision between a light particle
a and a nucleus X, may produce a light particle b and a nucleus Y:
X + a → Y + b
(9.90)
Such a two-body process is customarily written in the form X (a, b) Y. If the
particle b is the same as particle a, one has a scattering process. If the total
kinetic energy is unaltered in the collision, the scattering is elastic, whereas if
the total kinetic energy changes (generally decreases), the scattering is inelastic.
If b is different from a, we have a special case of nuclear reactions. All these
processes must satisfy certain conservation laws, such as charge conservation,
energy-momentum conservation, etc.
A nuclear reaction is usually accompanied by either a release or absorption
of kinetic energy. This is given by the difference between the total mass of the
particles before and after the collision. It is called the reaction energy or Q
value and is expressed as
Q =
i
f
i
f
m
m
−
∑ ∑
(9.91)
where m i and m f are the masses of the initial and final particles respectively,
normally expressed as rest energy in MeV. If Q is positive, energy is released in
345
235
238
( )
( )
N
t
N
t
≈ exp [– t (1/τ 235 – 1/τ 238 )]
(9.87)
Using the observed value of about 1/140 for the relative abundance,
t ≈
235 238
238
235
–
τ τ
τ
τ
ln 140
(9.88)
Since τ 235 ≈ 1.02 × 10
9
years and τ 238 ≈ 6.51 × 10
9
years, the age of the
elements is
t ≈ 5.98 × 10
9
years
(9.89)
This is in reasonable agreement with the age determined from the abundances
of other nuclei. It is also of the same order as the age of the universe deduced
from the rate of expansion of the universe (see Sec. 11.5), and hence is an
important element in the understanding of the universe.
9.6 NUCLEAR REACTIONS
The properties of a nucleus can be studied by bombarding it with energetic
particles, and analysing the consequences of the collisions. If the collision leads
to a nuclear interaction, it gives what is known as a nuclear reaction.
Usually, the projectile is a light particle, it may be a neutron, a proton, a
deuteron, an alpha particle or a photon (recently there has been considerable
interest in heavy ions as projectiles). A typical collision between a light particle
a and a nucleus X, may produce a light particle b and a nucleus Y:
X + a → Y + b
(9.90)
Such a two-body process is customarily written in the form X (a, b) Y. If the
particle b is the same as particle a, one has a scattering process. If the total
kinetic energy is unaltered in the collision, the scattering is elastic, whereas if
the total kinetic energy changes (generally decreases), the scattering is inelastic.
If b is different from a, we have a special case of nuclear reactions. All these
processes must satisfy certain conservation laws, such as charge conservation,
energy-momentum conservation, etc.
A nuclear reaction is usually accompanied by either a release or absorption
of kinetic energy. This is given by the difference between the total mass of the
particles before and after the collision. It is called the reaction energy or Q
value and is expressed as
Q =
i
f
i
f
m
m
−
∑ ∑
(9.91)
where m i and m f are the masses of the initial and final particles respectively,
normally expressed as rest energy in MeV. If Q is positive, energy is released in