Someproblemsdealwith the numberandrate ofdecays.You shouldknow the relationship
betweenthe decayconstantl, andthe halfJife T tn: T rp: ln2/)'. The halflife is often given but
you needtl-redecayconstantto carryout the calculation.ln an original collection ofNo nuclei,
the numberthat remainundecayedat the end of time t is given by N : N6e-n'.The activity rs
given by A : l"N and by A : ,4'6e-n',where,4,6is the activity at t : 0.
Questions and Example Problems from Chapter 31
QuestionI
Describedqualitativelyhow the radiusofthe daughternucleuscomparesto that ofthe parent
nucleusfor (a) crdecayand(b) p decay.Justifr your answersin termsofEquation31.2.
f- 2r (t.l*lD-'5* ) n^
/
\
| r
\ct ) a- arrya^+
(b)
n
f\
"j
ft=*Ye-+frx.ua^z*o
.a"aluq" + - Sw^tau,!r2
1 no r Ap-az^^t"a
---A db dl"ntfui)'+/4^'t&\d,,1rh
e rUc-r{
"t*-rat"-A*
V
Problem 1
for '?ljlb nna 1a;the net electricalchargeof the nucleus,(b) the numberof neutrons,(c) the
numberofnucleons,(d) the approximateradius of the nucleus,and (e) the nucleardensity.
+-
Aos DL -----) ga PfuYwdw
l"
la{D
fa.
|
,
Irtr
----
a _ ,. l , \
/^lL/
<4
'l d
-r (
l
'
l
"
l
d
'
5
n
'
,)
4/2"
=
M,t$-
sa,elre,^s
(o)
Q*r
= 8a ( l"t,oa*lD-'1c)
(b)
IAQ
(.)
r;Til
|,3t\ v lo-reC
/rur.,l;rzrrl
r a ( l.l.* lo-'5^) A'/t :
( d.)
r ^- ?. \r gD-'u.
le)
:
D = n/,,
/ V
\
n0^.,.1--.
A
----4$n13
l"""u*'A- =
'i/3n
(l-t"to-'^) A
Nn..l"'n
'--'/
fl3 n ( t.r*ro'5n,)3
Problem2
For the following nuclei, eachundergoingp- decan write the decayprocess,identiffing each
tlC and
'llfU
daughternucleus,with its chemicalsl,rnbolandvaluesfor Z and A: 1a;
1t;
I p-, j, u "-?e
Q aoca.{4:
{o.
tt tu/ \
'jN"-?.
|_-.4
t9
d-r o\
( 0)
n +2*ffiK'S
--^;\D*-?"
f)l
YN
oA
).iAo; u
B\t
t
'-'/
>?.lt
g"
rl.
o
12c+-1 e
Problem3
Determinethe symbol f X for the pmentnucleuswhosea decayproducesthe samedaughteras
the B-decayof thallium'?TTl.
Pd\
S.!.r,'A-)
A P----.+fi T)
d.r4d44 -+
.
_
A
,' n ---__5A_./
,'
_s
r
l-t
?^\1./'
z+l "
z'
.
.-
f
-r\
*-?.+(v-.)
1H"
^"Nt
,/
^;:7b'9 e
J attar';
-->
AtA g
t'l
lo
A P*--'
z'
&oF
ta
4^t+.
Ti pur
Pb+ {He
AJ ele
z ---'> 8l
P-aoa'
Problem4
Iodine 'l]I isused in diagnosticandtherapeutictechniquesin the treatmentof thyroid disorders.
tlll remainsafter
This isotopehas a hatflife of 8.04 days. What percentageof initial sampleof
30.0days?
T,/n = !.o1 days--:
= O"otba d&il
\
/
t \ . r . \ e . t , .)1_ U _ ' ) ( 3 A e a . r 4 t )
N = )\" g- \r:"""'
_\+
r |
D' 6?'z/t.o1so-"a
^ = ^yru^
N' No d^t-
N= (o"o?53)N"-)
7o /'e,4\\d'^a o|fit
1"53
^ i-
/cr!-Auw\'t
{-h
t\E
---
N,/N"r- O'0"53
3Daa4a
3o"o edc,-gz
^ 3o'"h,oq = 3.?3 9d4&,*,
,rla-$
Nv,r/.'Ui
='hn No probrem, N
fr
M %) '''"t P2
o^$& q Aa4-1ri'4
= (o'o_r5a ri")
N= /[r,.r No
The numberof radioactivenuclei presentat the startofan experimentis 4.60 x 10". The number
Whatis thehalf-life (in days)of the nuclei?
presenttwe ty dayslateris 8.14x 1014.
N o = 4'6o*lo'5
1rJ-;"tYrl6'Y
f = f,o.odoys
\
-l-
N=N.j^'
-\t
rr,
= e n
VN"
-D^(Vxr")=-\f
Ty"=3
^ / 3, tq* lO'u \
- bll4t;,r''
t
\
= o'oto6Aa,.,,-l
T'/,.=
,^a A
l" 1
O.oXtot"
.._-/
Problem6
Find the bindingenergy(in MeV) for lithium lli (atomicmass:7.016003 u)
\:-'7
Wq
t
+
,tl, ,F""L
futu* lua-p#." &**';i 8*
rvra+e$
00p - l. oo'le1hq
r06= 1.ootr61n5,
\-/
1LA = qZl"5 N"V
Po ,wt'u*"oa
---, 3 6:^.,u*, 1"*,,'n- ) 4 3-.ar'&,*.,w
t;
\
A m = l(loo"t>l ba) + U(,ooAu65u)
t 3 ( 5 , t " t l 5 . 7 q q rl o - Y u ) - J " o t b o o 3 L |
tl" -- 5"t,65?gl xldlq
-r
,"r'.'ovba'n 'z ffr'-q-''1J
*A0ff''uun ("1 'otpoo3J)Jru!-fu4
o{ Po tt'th^'"
for-;
}9te'/\{'aavAt4t*ty*a}r-u
"*b4=
,9-r+ bp1 = C$p * hr) * rile) - n0a"n
'p
-e,aA,lgr* Xa cd!-E Aj}." Igtt qv'eL:', d"ttii4t
A,n , C\l) -"*\
-)
/)m'\'
(Im)c^vrta
A:Ary.
\,t>lrnoo3q
Problem7
Mercury '?$Hg hasan atomicmassof 201.970617u. Obtainthe binding energyper nucleon(in
MeV/nucleon).
,6 ^wra*l
) ]f a',,rczrrra,ta
Jsr, a9t"h4 oLu&'o'{u
Sr = l. ooeA?6tt
p.|n= l.oo86{,59
{ , ,e1-\= 5 . 1 8 5 1 q 1 x 1 O l U
w'-aa4
(eut.q?or,'lu) n*-bAu1f
A tfl = (rqp * N6t f0") D,r^
*fi H.--
8o p"a:,,nlaA "rrzu#'r,a
8O ultfr-tw
N\u, = 3.ol.Q'tDtal?q
u) + To(5.q8'5'lql xto-qa)
A'fo = ?o ( l,oolarr,u)r | ))Cl.ootL{,5
- e.Dl" lrlobti Q r7f
l, 3'5 q
Arn = t.?rxEu / 13J:5-Uc!
) = I 815.1-tyr"V
'/
\
L'A
* fu,la,u AoA
WW
/\uuJtt'tq
= VHJ
aoa h'ailtY(6
=
l,trrtg^
Mt