Elements of Modern Physics
26
mass is no small that it is not possible to observe it directly. On the other hand,
for nuclear fusion or fission reactions, the change in the mass is quite substantial
and can be measured directly.
In the fusion of hydrogen nuclei into helium nuclei, which is the basic reaction
in stars, four protons combine either through the proton-proton cycle or the
carbon cycle (see Sec. 9.8) to yield a helium nucleus and two positrons.
4p → He 4 + 2e +
(1.89)
The change in the mass for this process can be obtained from
m(p) = 1.007277 µ, m (He
4
) = 4.001506 µ, m (e
+
) = 0.000549 µ
(1 µ = 1.6604 × 10
-27
kg), so that energy available is
(∆ m) c 2 = 24.7 MeV
(1.90)
The sun today is at a fairly stable stage of its evolution, called the main
sequence period. Assuming that the sun will remain on the main sequence till
about 10% of the hydrogen is burnt, since its mass is about 2 × 10
30
kg and it
contains about 75% of hydrogen by mass, the total energy to be released while
it is on the main sequence is about 8.9 × 10
43
J. The energy emitted by the sun
is about 3.9 × 10
26
J/s, so that its lifetime on the main sequence is approximately
7 × 10
9
years. This should be compared with the more detailed estimations of
1.1 × 10
10
years for the main-sequence lifetime of the sun, of which it has
already spent about 4.5 × 10
9
years.
Example 5
The transformation properties of the electric field due to a moving charge can in
principle be obtained from Eqs. (1.62) and (1.63) where
1
,
φ
c
A
transforms
as a four-vector. However, it is simpler to deduce them from the expression for
the Lorentz force in Eq. (1.61) and the transformation of force given in
Eq. (1.59).
Consider the field due to a charge q at the origin, moving with velocity u in
the x-direction. Then, the force on a unit charge at rest at P is
f = E
(1.91)
However, in a frame F′ which moves with velocity u, the charge is at rest
and therefore, the force on the unit charge is
f′ = E′
26
mass is no small that it is not possible to observe it directly. On the other hand,
for nuclear fusion or fission reactions, the change in the mass is quite substantial
and can be measured directly.
In the fusion of hydrogen nuclei into helium nuclei, which is the basic reaction
in stars, four protons combine either through the proton-proton cycle or the
carbon cycle (see Sec. 9.8) to yield a helium nucleus and two positrons.
4p → He 4 + 2e +
(1.89)
The change in the mass for this process can be obtained from
m(p) = 1.007277 µ, m (He
4
) = 4.001506 µ, m (e
+
) = 0.000549 µ
(1 µ = 1.6604 × 10
-27
kg), so that energy available is
(∆ m) c 2 = 24.7 MeV
(1.90)
The sun today is at a fairly stable stage of its evolution, called the main
sequence period. Assuming that the sun will remain on the main sequence till
about 10% of the hydrogen is burnt, since its mass is about 2 × 10
30
kg and it
contains about 75% of hydrogen by mass, the total energy to be released while
it is on the main sequence is about 8.9 × 10
43
J. The energy emitted by the sun
is about 3.9 × 10
26
J/s, so that its lifetime on the main sequence is approximately
7 × 10
9
years. This should be compared with the more detailed estimations of
1.1 × 10
10
years for the main-sequence lifetime of the sun, of which it has
already spent about 4.5 × 10
9
years.
Example 5
The transformation properties of the electric field due to a moving charge can in
principle be obtained from Eqs. (1.62) and (1.63) where
1
,
φ
c
A
transforms
as a four-vector. However, it is simpler to deduce them from the expression for
the Lorentz force in Eq. (1.61) and the transformation of force given in
Eq. (1.59).
Consider the field due to a charge q at the origin, moving with velocity u in
the x-direction. Then, the force on a unit charge at rest at P is
f = E
(1.91)
However, in a frame F′ which moves with velocity u, the charge is at rest
and therefore, the force on the unit charge is
f′ = E′