The urrified atomic mass unit (u) is defirled to be 1/12 drat of the mass ofone atom ofcarbon12 whete the mass of caJbori'12 is defined to be exacdy 12 u.
a. Determine the average mass of a nucleon in carbon_12 in units of kg if the mass of carbon12 is 1.993 x 10'26 kg.
b. Convert the mass in kg to mass in urrits of MeV/c2.
t - t,\L
z
E-
-*
t
I^a(J --
.
lt6tok+tc-9c<
t^^arj
€ __ l.lqLt?.t_to-,J
a.
b.
2.
=
l.,11Lt1..ttb )
t.6 +D-'q J/eV
73q ? a, Ot* -V
The avemge mass ofa nucleon in catbon-12 is 1.66 x 10_27 kg
The average mass of a nucleon in carbon- 72 is 934 Me'l /c2.
The mass of a hel.ium-4 nudeus is 4.0026 u. The mass of an rndividual Proton is 1 .0073 u and
1.0087 u for a neutfon. Determifle mass defect of tle heliurn nucleus.
A He nucleus made up of2 Plotoos 2nd 2 rieutlons:
frn = 2P* + ?a
Zv = 2(t.0o73 ,) + z( t us+ )
- 1.1)tL t4
A i^^ = Ll.Ol 2,,-(
-
L1@26
- = A. ozqq q
The mass defect is 0.0294 u.
Problems
Detemine the mass-energy equivalence of
L: ,-
a
Ptoton at test in units of electron volts. [939 MeU
mc"
tl)
= ( t, rol x\ci'zr q3\(3 ooxroB ""'
: \'Eio3xrci'o T
; \.60x to '1 j /*: v
z
= 9 st,alSpoO
-q3cl !
c
\Qb
Chaptei
8
cV
- 333
Determine the maximum mass that can be created, in units of kg, from '1.025 MeV of eflergy.
[1.82 x 10-30 kg]
l.oa5 x rD!.eV x l.bo,(
=\
tD-t'1
E=
fi
eV
rncz
*'=
Uq x\o-\3J
9
az
:
3.
bq xro '35.
(-l co - r c* -\') I
.
= l.EZxrb-3.ES
A muon is a particle that is 207X heaviet than an electron and has a charge of-1. Detetmine the
mass ofa muon in units of MeV/c2. [100 MeV/c2]
ffi =- ?'o-1 tq.rt x ro'3'\.5\
: \.t65-l-t x lo tl \tJ
-(i.SStt't x rda q) ( 3.oc".rc/r-\!),'
= 1.9n1 xro 5
: \ 'k' \ to-'(" C
;
IOG' l''\€
V
Ttre mass of a neutino has never been measured but it is theorized that a neutrino may have a
mass as high as 50 eV /c2. Convert 50 e\ /c2to units ofkg. [8.9 x 10-3s kg]
fn= E
Ecc! ( l.bC'xl$-'s r/<v)
t3.oo, I os w\ls-.)'
: B,tl )^ to-3c, \g
5.
Complete tlle chan below. fAppendix A]
A.
b.
Particle
Rest Mass Qg)
electron
9.1096
x
10-31
1.6126
x
10'21
1.6149 x 10 27
Rest Mass (u)
Resr Mass
j9 y ro-r ':
t,o I
r.o
D.5iL
qqt
5.
I
(MeV/c)
9r?-
To convett to atomic mass units divide the mass in kg by 1.66 x 10-27 kg/u.
To conr,e$ to MeV/c2, fust r.rse E = mcz to calculate energy in joules. Then convert to
energy in eV.
Copyrighr @ Kennedy/Oswald, @ 2008
Chapter
8
- 334
I
6.
Use the followiag fusion reactioo to determine the amount ofrnass that is coaverted to energy.
[3.13
x 1O'4 kgl
:H +iH
-______________+
__
;He
jn +
+
17.6
ltev
l-l .G x l06 e-V (r'oc, a Lo-"'5/e!)
a,-
(
?
o<,
r rog.r'ls)L
= 3,\3 x \o-.7 L3
Ute the inJornation below la awucr
'When
quttiaw 7
b
8.
positron and electron collide they destroy each other and two gamma photons ate qpically
produccd (a.ka. pair aanihilation). Assume a positron and electron are each ttavelling at 8.91 x 107 rn/s
wheo they collide head-on as shown in the diagram below.
a
photon
+2
photon
7.
Assumc that each photon equally shares dre rest masses ofthe positron and electtoo aod their
y'ffi::-ii#"trfff.ru.ro,.*.,..ouision.[3.62x10'r5J]
flffi;fl
: H;:"T;?,?:Jl;T"'*1L',:r"":
Hi1T,*i,i"*1ll;lifl #-J-.*, ffi
Hz)
11.29
x
6--64
1o2o
cL, Eo= * n-rvz
=
l; (e.rrxrc B'\)(8.9 t^tor,-rls)L
=3,Ga xlu
rnc" -, (a.rrx1o a,t3)(3,oo
b,
E=
c.
E=3,CLxto-'sTl z. 2a ,^ to 'q T
= 8.5boro X lU ,qT
CopFighr O KeDrcdy/ossald,
@ 2008
rs-
5
r. tov
mls)L = 8,20vro "rf-
€-- E-_
h
g ,rr661e
;r,
1O-'+f
6,b:3xroll.s
l'29 ,r ttr'' Hz
Chaptcr
8
- 335
Explain why a siagte photon caoaot be produced from
the collieion. [Appendix A]
It u:oo rcl no1 c,be:)
o( aY") or-Y) er$u 'r r
r1.\a I o--rf, o+
().-:.4-e- wc^:hsr,
<
.
9.
By expcrimeat, using a mass spccrometer, the mass ofhydtogea-2
has been determioed to be
2.014 102 u But if the irdividuat masses oi th. p^
wcre mathernatically summed, a mass of 2.0t e l'gt
is oltaioea. O"LrloLJ,},-JBi"aiog .".rg),
"
of the deuteriuro atom ia eV. [223 MeV]
d.r;;i;;.-;;rru"ir*.*r_, *..
4
a .O Ib q q
rn '
r
!, - 2 or!iroZo 1 O,bo23B.-1
x \.
€=
n{z
-'
(3lbs1,1 Ir..,
b," x
ro'"
.oE5)(3.qr.,".1;y{59
3.at"s x ro. '37
a a?o
': l.(,O X I o-rq f, /e \,/
10.
(.J
q/,
)'tq r'
Tzci<\
= a,e3 He!
The mass of a helium-4 nucleus is 4.0026 u, The rnass of
an individual proton is 1.0073 u and
1 .0082 u for a aeutton. Detetmine
the binding .r.r$, p..
i.iiuu, ooa.u, oott"
of ev per ouctcod- [6 86 MeV/nucreon]
;;;;o;;1f,;
;.-, ; ;:"._::.-;",.*.'
acn= E (t.oorr.r) t ) (r.oc rz"\= O,ozqq.r x l. Gb ^ lo- t-l .EsOq x Lo- tt oJ
-t.oo z.6 .r
21
4/o
E = r.,c z
=
(q,t(c,i r r b- zi rJ (3,u:n
= Ll,3q x lu-,27
= e'1,r5aa5-o
1
Copy4hr
@
Kennedy/Osq,ald,
tl
:
tDe
rnls)z
\,LeO x tb- 'cT/eU
n..rct<,-,"s
= 68b 3ub 3
- 6,8{e HeV
/
'zi.rc)
core
i'
('
Ur
the
)n;famator
below la anm,er
As the binding energy per nucleon increases,
the stability ofthe nucleus rncreases. Elements
'with ifltemediate mass numbers have dre
greatest binding energy pet nuclear particle.
qrution 11.
(issi.-
Y>
EA
o
100
Mass number
The maximum value of approximately 8.8 MeV per nucleon occurs in the vicinity of mass number 56.
1 1
.
12.
Identif] the region of the graph where elements
a. fusion. fAppendlx A]
b. Ession. [Appefldk A]
may undetgo
pair production, a high-energy photon is converted into a particle and its
antiparticle (e.g., ao electron and a positron). This energy to mass convelsion can occur
according to the equation, E = mc2. Explain why both charged particles must be Prcduced and
flot just a single p2nicle. [Appendk A]
In
a process called
Lo-- oi
Co
r'\;q".vcJro"t : t
11n.,.-. y)Ol !-) .,- f
Use the
inJomatiot
o.-,-r
cl
<--!'\c.--g
c,\.
a a.b"r r.es
- piq- ti c] C (!!- < P.oc\\Jur'l'
below lo a,$aer qrestiafl 13.
A common trait for all cultures is to obseffe natural phenomena and aftemPt to interPret them. The
woddview of First Nation peoples in Nor*r Amenca is to relate or unifi, apparently different
phenomena. The desirc to relate apparendy diffetent natural phenomena has also been an exttemely
important motivator in modern physics.
13.
Describe the elfots ofphysicists in the 19d and 20$ ceatu4' to
phenomena. [Appendix A]
unifi
apparendy diffetent
\ Y-r\.'-i,1 *'f) s rv1
(>)-;\((\- .ro.tr'.-3
H c.xr^..<-t \ -/ e \€ cl-ro YYrc5 r r-e)'i s r-w> r e rn (?
C"p,.isht
€
tn'3lc.rrl -) vY)c\s:> r
@
K""r.dyl5swa1d,
@ 2008
r'-1-\e'-
5J
Chapter
8
- 337