Environmental Engineering Reference
In-Depth Information
which reduces to the familiar
1
2
m
A
v
A
+
1
2
m
B
v
B
=
1
2
m
C
v
C
+
1
2
m
D
v
D
(7.29)
if we assume
m
A
+
m
D
. It is very important to remember that this
formula is only a good approximation if all speeds are small enough compared to
the speed of light.
In contrast, Einstein's theory does not require the conservation of mass: it only
requires that the sum of kinetic and static energy be conserved. We subsequently
refer to the static energy as the 'rest mass energy', it is the energy possessed by a
particle at rest:
m
B
=
m
C
+
mc
2
.
E
rest
=
(7.30)
The kinetic energy is then defined to be the difference between the total energy
and the rest mass energy:
1
)mc
2
.
=
=
−
E
kinetic
K
(γ (u)
(7.31)
Example 7.1.1
What is the rest mass energy of an electron?
10
−
31
kg and so using Eq. (7.30)
Solution 7.1.1
The mass of an electron is
9
.
11
×
it possess an energy equal to
mc
2
10
−
14
J.
E
rest
=
=
8
.
19
×
It is almost always the case that it is more sensible and more convenient to express
energies in electronvolt (eV) units rather than in joules. One electronvolt is the
kinetic energy acquired by an electron that has been accelerated through a potential
difference of 1 volt, i.e.
10
−
16
J.
=
×
1
eV
1
.
60
The rest mass energy of an electron in these units is then given by
10
−
14
8
.
19
×
E
rest
=
10
−
16
eV
=
0
.
511
MeV.
1
.
60
×
Thus an electron has a mass energy equivalent to just above one half million electron
volts.
Also worth noting is that particle and nuclear physicists quite often quote particle
masses in eV-based units, mainly because it is irksome to keep explicitly dividing
by the speed of light squared. For example, one might say that an electron has a
mass of 0.511 MeV
/c
2
. Similarly momenta might typically be expressed in units
of MeV
/c
.
