Lecture
5
•  Jan.
20
•  Rela1vity
II
h7p://aniketjha.blogspot.com/2010/07/emc2.html
i‐clicker
Quiz
(Jan.
18)
•
An
electron
and
positron
with
equal
and
opposite
momenta
collide
head
on
and
annihilate
into
2
photons,
each
measured
with
1.022
MeV
energy.
What
is
the
invariant
mass
of
the
interac1on?
me
=
0.511
MeV/c2
A)  0
B)  me
C)  2me
D)  4me
How
much
energy
would
be
required
to
accelerate
a
par1cle
of
mass
m
from
rest
to
a
speed
of
0.5
c
?
Express
the
answer
as
a
mul1ple
of
the
rest
energy.
Ei = mc
E f = γ mc 2
2
ΔE = E f − Ei = (γ − 1) mc 2
ΔE = 0.155mc
γ = 1.155
2
3
At
what
value
of
u/c
does
the
measured
mass
of
a
par1cle
exceed
its
rest
mass
by
11%
?
γ = 1.11 =
1
1− β2
1
1− β =
= 0.9009
1.11
2
β 2 = 1 − ( 0.9009 )
2
β = 1 − ( 0.9009 ) = 0.434
2
4
How
much
work
must
be
done
on
a
proton
to
increase
its
speed
from
0.1c
to
0.2c
?
(The
rest
energy
of
a
proton
is
938.3
MeV.)
E1 = γ 1mc 2
γ 1 = 1.0050
γ 2 = 1.0206
E2 = γ 2 mc 2
ΔE = (γ 2 − γ 1 ) mc 2 = Δγ mc 2
= 0.0156mc 2
ΔE = 14.7eV
5
A
proton
with
rest
energy
of
938
MeV
has
a
total
energy
of
1000
MeV.
(a)
What
is
the
value
of
u/c?
(b)
What
is
the
proton's
momentum?
Express
your
answer
in
units
of
MeV/
c
E = γ mc 2 = 1000MeV
γ =
1000MeV
= 1.0661
938MeV
(
E = ( pc ) + mc
2
2
( pc )
2
(
)
2 2
= E − mc
2
β = 1 − 1 / γ 2 = 0.3466
)
2 2
= (1000MeV ) − ( 938MeV )
2
2
pc = 347MeV
p = 347MeV / c
6
Find
the
energy
that
is
needed
to
remove
one
proton
from
a
4He
atom,
leaving
a
3H
atom
plus
a
1H
atom.
(Assume
atomic
mass
of
3H
=
3.016
amu,
atomic
mass
of
4He
=
4.0026
amu,
rest
energy
of
proton
=
938.272
MeV,
atomic
mass
of
1H
=
1.00794
amu.)
ΔE = m
( H )c
3
2
( )
+ m 1 H c2 − m
(
4
)
He c 2
= ( 3.016 + 1.00794 − 4.0026 ) ( 931.5MeV )
= 19.9MeV
7
The
energy
released
in
the
fission
of
a
235U
nucleus
is
about
200
MeV.
How
much
rest
mass
(in
kg)
is
converted
to
energy
in
the
fission
of
1000
kg
of
235U?
N = N A 1000kg / ( 235g / M ) = 2.8x10 27
E = N × 200MeV = 5.6 × 10 35 eV
(
)
E = 5.6 × 10 35 eV 1.6 × 10 −19 J / eV = 9 × 1016 J
m = E / c 2 = 1kg
8
i‐clicker
Quiz
(Jan.
20)
•
An
electron
has
a
momentum
equal
to
1
MeV/c.
What
is
its
total
energy?
A)  0.56
MeV
B)  1.12
MeV
C)  2.24
MeV
me
=
0.511
MeV/c2