YouTube Lecture # 68

1. 1
Find the momentum of
(a) a 10.0-MeV gamma ray;
(b) a 25-keV X ray;
(c) a 1.0-μm infrared photon;
(d) a 150-MHz radio-wave photon.
Express the momentum in kg·m/s and eV/c.
Helping Tools
No.1

2. 2
No.2

3. 3
No.3

4. 4
No.4

5. 5
Solution
(a)
6
7 7 19
12
10.0 10 10
10 10 1.602 10
1.602 10
E MeV X eV
eV X X J
X J
−
−
= =
= =
=

6. 6
8 8
7 7 12
12
20
8
20 21
10 10 1.602 10
1.602 10
,
3.00 10 3.00 10
.
0.534 10 .
3.00 10
. .
0.534 10 5.34 10
E
Also p
m m
c c X X
s s
N m
X N s
m
X
s
e
kg m kg m
X X
s s
V eV X J
X −
− −
−
−
= = = =
= =
= =

7. 7
(b)
19
19 15
3
25.0 k 25.0 10
25000 25000 1.602 10 J
=40050X10 J=4.00X10 J
E eV X eV
eV X X −
− −
= =
= =

8. 8
8
15
15
8
23
8
23 23
25000 25000 4.00 10
4.00
,
3.00 10 3.00 10
.
1.333 10 .
3.00 10
. .
1.333 10 1.333
10
10
E
Also p
m m
c c X X
s s
N m
X N s
m
X
s
e
kg m kg m
X X
s
V V X
s
e J
X −
−
−
−
−
= = = =
= =
= =

9. 9
(c)
6
34 34
6 6
28 28
1.0 1.0 10
6.626 10 J. 6.626 10 N.m.
1.0 10 1.0 10
.
6.626 10 . 6.626 10
m X m
h X s X s
p
X m X m
kg m
X N s X
s
 

−
− −
− −
− −
= =
= = =
= =

10. 10
6
15
9
6
8
9
1
1.0 1.0 10
4.136 10 eV. .
4.136 10
1.0 10
2.998 10
.
4.136 10
12.399728 10 1.2399728 1.2
m X m
h X s eV s
p X
X m m
m
X
eV s s
X X
m c
eV eV eV
X
c c c
 

−
−
−
−
−
−
= =
= = =
=
= = 

11. 11
(d)
15 6
9 7
4.136 10 . 150 10
620.4 10 6.204 10
hf X eV sX X Hz
p
c c
X eV X eV
c c
−
− −
= =
= =

12. 12
15 6
9 7
7 19
8
34 34
34
4.136 10 . 150 10
620.4 10 6.204 10
6.204 10 1.602 10
2.99792458 10
.
3.315 10 3.315 10 .
.
3.315 10
hf X eV sX X Hz
p
c c
X eV X eV
c c
X X X J
m
X
s
J s
X X N s
m
kg m
X
s
−
− −
− −
− −
−
= =
= =
=
= =
=
The End