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1
PHYSICS CHAPTER 15
is defined as the spontaneousis defined as the spontaneousdisintegration of certaindisintegration of certain
atomic nuclei accompanied byatomic nuclei accompanied by
the emission of alphathe emission of alpha
particles, beta particles orparticles, beta particles or
gamma radiation.gamma radiation.
CHAPTER 15: RadioactivityCHAPTER 15: Radioactivity(3 Hours)(3 Hours)
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PHYSICS CHAPTER 15
2
At the end of this chapter, students should be able to:At the end of this chapter, students should be able to:
ExplainExplain,,++,,andand decays.decays. StateStatedecay law and usedecay law and use
DefineDefineactivity,activity,AAand decay constant,and decay constant, .. Derive and useDerive and use
DefineDefinehalf-life andhalf-life and useuse
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ys
ics 15.1 Radioactiv# d#cay (% "ours)
Ndt
dN=
teNN
= 0t
eAA = 0!"!"
2ln
2/1 =T
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PHYSICS CHAPTER 15
3
'iitio (r#'#r to s#ctio 1.1.3).
T"# radioactiv# d#cay is a spontaneousspontaneousr#actio t"at
is unplannedunplanned* cannot be predictedcannot be predictedad
independentindependento' physical conditionsphysical conditions(suc" as
!r#ssur#* t#!#ratur#) ad chemical changeschemical changes. T"is r#actio is randomrandomr#actio +#caus# t"#
probabilityprobabilityo' a nucleus decayingnucleus decayingat a ,iv# istat
is t"# samesame'or a-- t"# uc-#i i t"# sa!-#.
Radioactiv# radiatios ar# #itt#d w"# a usta+-#uc-#us d#cays. T"# radiatios ar# alpha particles,alpha particles,
beta particles and gamma-raysbeta particles and gamma-rays.
#$.# "adioactive decay
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PHYSICS CHAPTER 15
4
A a-!"a !artic-# cosists o'two protons and two neutronstwo protons and two neutrons.
It is id#tica- to a helium nucleusa helium nucleusad its sy+o- is
It is positively chargedpositively charged!artic-# ad its va-u# is %# wit" ass
o' .//%0/3 u.
"# a uc-#us ud#r,o#s a-!"a d#cay it -os#s 'our uc-#os*
two o' w"ic" ar# !rotos* t"us t"# r#actio ca +# r#!r#s#t#d
+y ,##ra- #2uatio +#-ow:
Ea!-#s o' d#cay :
#$.#.# Alpha particle % &
He42 424R
Q++ HePbPo 4221482
21884
%'arent&%'arent& %%particle&particle&
%Daughter&%Daughter&X
A
Z +Y
4
2
A
Z + QHe4
2
Q++ HeRaTh 422268823090
Q++ HeRnRa 4222286
22688
Q++ HeThU 422349023892
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PHYSICS CHAPTER 15
5
#ta !artic-#s ar#electrons or positronselectrons or positrons(so#ti#s is ca--#d
+#ta6ius ad +#ta6!-us !artic-#s).
T"# sy+o-s r#!r#s#t t"# +#ta6ius ad +#ta6!-us (!ositro)
ar# s"ow +#-ow:
(eta-minus(eta-minus!artic-# is negatively chargednegatively chargedo' 1# ad its ass#2ua-s to t"# mass of an electronmass of an electron.
(eta-plus %positron&(eta-plus %positron&is positively chargedpositively chargedo' 1# (ati!artic-#o' #-#ctro) ad it "as t"# sa#
mass as the electronmass as the electron.
I +#ta6ius d#cay* a #-#ctro is #itt#d* t"us t"# massmass
number does not charge but the charge of the parentnumber does not charge but the charge of the parent
nucleus increasesnucleus increasesby oneby oneas s"ow +#-ow:
#$.#.) (eta particle % &
e
0
1
4R
e
0
1
+
4R
#ta6ius#ta6ius
(#-#ctro) :(#-#ctro) :
#ta6!-us#ta6!-us
(!ositro) :(!ositro) :
%'arent&%'arent& %%%Daughter&%Daughter&XAZ +Y1
AZ
+ + Qe01
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PHYSICS CHAPTER 15
6
Ea!-#s o' ius d#cay:
I +#ta6!-us d#cay* a !ositro is #itt#d* t"is ti# t"# c"ar,# o'
t"# !ar#t uc-#us d#cr#as#s +y o# as s"ow +#-ow:
7or #a!-# o'
!-us d#cay is
Q++
ePaTh 0
1
234
91
234
90
Q++ eUPa 0
123492
23491
Q++ ePoBi 0
121484
21483
%'arent&%'arent& %'ositron&%'ositron&%Daughter&%Daughter&
XAZ +Y1A
Z + Qe01
Qv +++ enp 0110
11
*eutrino*eutrinois unchargeduncharged
particle with negligibleparticle with negligible
massmass.
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PHYSICS CHAPTER 15
7
8aa rays ar# high energy photonshigh energy photons(electromagneticelectromagnetic
radiationradiation). Eissio o' ,aa ray does not change the parent nucleusdoes not change the parent nucleus
into a different nuclideinto a different nuclide* sic# #it"#r t"# c"ar,# or t"#uc-#o u+#r is c"a,#d.
A ,aa ray !"oto is #itt#d w"# a nucleus in an excitednucleus in an excited
state ma+es a transition to a ground statestate ma+es a transition to a ground state. Ea!-#s o' d#cay ar# :
It is uncharged %neutral& ray and ero massuncharged %neutral& ray and ero mass.
T"# differ between gamma-rays and x-rays of the samediffer between gamma-rays and x-rays of the same
wavelengthwavelengtho-y i t"# a#r i w"ic" they are producedthey are produced9
gamma-raysgamma-raysar# a result of nuclear processesresult of nuclear processes* w"#r#as x-x-
rays originate outside the nucleusrays originate outside the nucleus.
#$.#. amma ray % &
++ HePbPo 4221482
21884
++ eUPa 01
23492
23491
+ TiTi 2088120881
amma rayamma ray
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PHYSICS CHAPTER 15
8
Ta+-# 15.1 s"ows t"# co!ariso +#tw## t"# radioactiv#
radiatios.
#$.#./ 0omparison of the properties between alpha
particle, beta particle and gamma ray.
A-!"a #ta 8aa
C"ar,#
'-#ctio +y#-#ctric ada,#tic 'i#-ds
Ioiatio !ow#r
P##tratio !ow#r
A+i-ity to a''#ct a!"oto,ra!"ic !-at#
A+i-ity to !roduc#
'-uor#sc#c#
1)e1)e #e !" 1#e#e !" 1#e 2 %uncharged&2 %uncharged&
3es3es 3es3es *o*o
StrongStrong 4oderate4oderate 5ea+5ea+
5ea+5ea+ 4oderate4oderate StrongStrong
3es3es 3es3es 3es3es
3es3es 3es3es 3es3es6able #$.#6able #$.#
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PHYSICS CHAPTER 15
9
7i,ur#s 15.1 ad 15.% s"ow a d#'-#ctio o' * ad i#-#ctric ad a,#tic 'i#-ds.
7igure #$.#7igure #$.#
B
++++++++
E
7igure #$.)7igure #$.)
Radioactiv#
sourc#
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PHYSICS CHAPTER 15
10
;aw o' radioactiv# d#cay stat#s:
7or a radioactive source, the decay rate is directly7or a radioactive source, the decay rate is directly
proportional to the number of radioactive nucleiproportional to the number of radioactive nucleiNNremaining in the sourceremaining in the source.
i.#.
R#arra,i, t"# #2. (15.1):
H#c# t"# decay constantdecay constantis d#'i#d as the probability that athe probability that a
radioactive nucleus will decay in one secondradioactive nucleus will decay in one second. Its uit is ss##
.
#$.#.$ Decay constant % & dt
dN
Ndt
dN
Ndt
dN=
*egative sign*egative sign#as t"# number ofnumber of
remaining nuclei decreases with timeremaining nuclei decreases with time
Decay constantDecay constant
%#$.#&%#$.#&
N
dt
dN
=nucleieradioaci!re"ainin#o$nu"ber
raedeca%=
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PHYSICS CHAPTER 15
11
T"# d#cay costat is a c"aract#ristic o' t"# radioactiv# uc-#i.
R#arra,# t"# #2. (15.1)* w# ,#t
At ti# t=t=00,,N=NN=N00(initial number of radioactive nucleiinitial number of radioactive nucleii t"#
sa!-#) ad a't#r a timetime tt* t"# number of remaining nucleinumber of remaining nucleiis
NN. It#,ratio o' t"# #2. (15.%) 'ro t=0to ti# t:
dtN
dN = %#$.)&%#$.)&
=tN
N
dtN
dN
00
[ ] [ ]tNN
tN 00ln =
tN
N =0
ln
teNN
= 0Exponential law ofExponential law of
radioactive decayradioactive decay%#$.&%#$.&
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PHYSICS CHAPTER 15
12
7ro t"# #2. (15.3)* t"us t"# ,ra!" o'N* t"# u+#r o'
r#aii, radioactiv# uc-#i i a sa!-#* a,aist t"# ti# tis
s"ow i 7i,ur# 15.3.
teNN
= 0
2
0N
0N
4
0N
16
0N8
0N
2/1T 2/12T 2/13T 2/14T 2/1&T0t'i"e
N
li$ehal$(2/1 T
7igure #$.7igure #$.
Stiu-atio 15.1
*ote:*ote:
7ro t"# ,ra!" (d#cay curv#)*t"# life of any radioactivelife of any radioactive
nuclide is infinitynuclide is infinity* t"#r#'or# to
ta-k a+out t"# -i'# o' radioactiv#
uc-id#* w# r#'#r to its half-lifehalf-life.
http://opt/scribd/conversion/tmp/scratch2504/G:/P&P/Semester1/Latest/p11_01_01_01a.swfhttp://opt/scribd/conversion/tmp/scratch2504/G:/P&P/Semester1/Latest/p11_01_01_01a.swfhttp://af_4409.html/8/12/2019 Matriculation Physics Radioactivity.pdf
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PHYSICS CHAPTER 15
13
is d#'i#d as the time ta+en for a sample of radioactivethe time ta+en for a sample of radioactive
nuclides disintegrate to half of thenuclides disintegrate to half of the initial number of nucleiinitial number of nuclei. 7ro t"# #2. (15.3)* ad t"# d#'iitio o' "a-'6-i'#*
w"# * t"us
T"# half-life of any given radioactive nuclidehalf-life of any given radioactive nuclideis constantconstant* it
does not depend on the number of remaining nucleidoes not depend on the number of remaining nuclei.
#$.#.8 9alf-life %T1/2
&
teNN = 0
2/1Tt=2
) 0N
N=
2/1
00
2TeNN =
2/12 Te=
2/1
21 Te =
2/1ln2ln Te=
T 693*02ln2/1 ==9alf-life9alf-life %#$./&%#$./&
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PHYSICS CHAPTER 15
14
T"# uits o' t"# "a-'6-i'# ar# secondsecond(s)* minuteminute(i)* hourhour
("r)* dayday (d) ad yearyear(y). Its unit depend on the unit of decayunit depend on the unit of decay
constantconstant. Ta+-# 15.% s"ows t"# va-u# o' "a-'6-i'# 'or s#v#ra- isoto!#s.
6able #$.)6able #$.)
sotope 9alf-life
.5 1/
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PHYSICS CHAPTER 15
15
+econdperdeca%+10,3-i1 10
. =
is d#'i#d as the decay rate of a radioactive sample.the decay rate of a radioactive sample.
Its uit is number of decays per secondnumber of decays per second.
4t"#r uits 'or activity ar# curiecurie (0i0i) ad bec;uerelbec;uerel((;(;) > S.I.
uit.
?it cov#rsio:
R#-atio +#tw## activity (A) o' radioactiv# sa!-# ad ti# t:
7ro t"# -aw o' radioactiv# d#cay :
ad d#'iitio o' activity :
#$.#.< Activity of radioactive sample %A&
dt
dN
+econdperdeca%1B.1 =
Ndt
dN=
dt
dNA =
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PHYSICS CHAPTER 15
16
T"us
00 NA =
NA = ad teNN = 0( )teNA = 0
teAA = 0
Activity at timeActivity at time tt Activity at time,Activity at time,
tt=2=2
ad( ) teN = 0
%#$.$&%#$.$&
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PHYSICS CHAPTER 15
17
A radioactiv# uc-id# A disit#,rat#s ito a sta+-# uc-id# . T"#
"a-'6-i'# o' A is 5./ days. I' t"# iitia- u+#r o' uc-id# A is1./ 1/%/* ca-cu-at# t"# u+#r o' uc-id# a't#r %/ days.
Solution :Solution :
T"# d#cay costat is ,iv# +y
T"# u+#r o' r#aii, uc-id# A is
T"# u+#r o' uc-id# A t"at "av# d#cay#d is
T"#r#'or# t"# u+#r o' uc-id# 'or#d is
Ea!-# 1 :
QBA +
0*&2ln=
da%+20)101*0da%+)0*& 2002/1 === tNT
2/1
2ln
T=
1da%+139*0 =
t
eNN
= 0 ( ) ( ) ( )20139*020
100*1
= eN nuclei102*6 18=1820 102*6100*1 =
nuclei1038*9 19=
nuclei1038*9
19
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PHYSICS CHAPTER 15
18
a. Radioactiv# d#cay is a rado ad s!ota#ous uc-#arr#actio. E!-ai t"# t#rs rado ad s!ota#ous.
+. =/@ o' a radioactiv# su+stac# d#cays i ./ days. t#ri#
i. t"# d#cay costat*
ii. t"# "a-'6-i'# o' t"# su+stac#.
Solution :Solution :
a. Rado #as t"at t"# time of decay for each nucleustime of decay for each nucleus
cannot be predictedcannot be predicted. T"# probability of decay for eachprobability of decay for each
nucleus is the samenucleus is the same.
S!ota#ous #as it happen by itself without externalhappen by itself without external
stimulistimuli. T"# decay is not affected by the physical conditionsdecay is not affected by the physical conditions
and chemical changesand chemical changes.
Ea!-# % :
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PHYSICS CHAPTER 15
19
Solution :Solution :
+. At ti#
T"# u+#r o' r#aii, uc-#i is
i. y a!!-yi, t"# #!o#tia- -aw o' radioactiv# d#cay* t"us t"#
d#cay costat is
ii. T"# "a-'6-i'# o' t"# su+stac# is
da%+'0*4=t
= 0010080 NNN
nuclei2*0 0N=
teNN = 0 ( )0*4002*0 = eNN( )0*42*0 =e
( )0*4ln2*0ln = e
1da%402*0 =( ) eln0*42*0ln
=
2ln2/1 =T
402*0
2ln2/1 =T
da%+,2*12/1 =T
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PHYSICS CHAPTER 15
20
P"os!"orus63% is a +#ta #itt#r wit" a d#cay costat o' 5.0 1/
s1. 7or a !articu-ar a!!-icatio* t"# !"os!"orus63% #its ./ 1/
+#ta !artic-#s #v#ry s#cod. t#ri#
a. t"# "a-'6-i'# o' t"# !"os!"orus63%*
+. t"# ass o' !ur# !"os!"orus63% wi-- ,iv# t"is d#cay rat#.
(8iv# t"# Avo,adro costat* BA0./% 1/%3o-1)
Solution :Solution :
a. T"# "a-'6-i'# o' t"# !"os!"orus63% is ,iv# +y
Ea!-# 3 :
2ln2/1 =T
1,1, +104*0)+106*& ==dt
dN
,106*&
2ln
=
+1024*1
6
2/1 =T
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PHYSICS CHAPTER 15
21
Solution :Solution :
+. y usi, t"# radioactiv# d#cay -aw* t"us
0./% 1/%3uc-#i o' P63% "as a ass o' 3% ,
.1 1/13uc-#i o' P63% "as a ass o'
1,1, +104*0)+106*& ==dt
dN
0Ndt
dN=
( ) 0,, 106*&100*4 N=nuclei1014*, 130 =N
32
1002*6
1014*,23
13
#1080*3 9=
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PHYSICS CHAPTER 15
22
A t"oriu6%%= isoto!# w"ic" "as a "a-'6-i'# o' 1.
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PHYSICS CHAPTER 15
23
Solution :Solution :
+. y usi, t"# uit cov#rsio ( -ideca%/+econd )*
t"# activity is
Sic# t"#
I' 0./% 1/%3uc-#i o' T"6%%= "as a ass o' %%= , t"us
3.=0 1/1
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PHYSICS CHAPTER 15
24
Solution :Solution :
c. I' %%= , o' T"6%%= cotais o' 0./% 1/%3uc-#i t"us
15./ , o' T"6%%= cotais o'
T"#r#'or# t"# u+#r o' #itt#d a-!"a !artic-#s !#r s#cod is
,iv# +y
( )231002*6228
0*1&
nuclei1096*3 22=N
( ) 228 1096*3101&*1 = N
dt
dNA ==
+econdparicle+/10&&*4 14 = A
I,or#d it.
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PHYSICS CHAPTER 15
25
At the end of this chapter, students should be able to:At the end of this chapter, students should be able to:
ExplainExplainthe application of radioisotopes as tracers.the application of radioisotopes as tracers.
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PHYSICS CHAPTER 15
26
#$.).# "adioisotope is d#'i#d as an isotope of an element that is radioactivean isotope of an element that is radioactive. It is !roduc#d i a uc-#ar r#actor* w"#r# stable nuclei arestable nuclei are
bombarded by high speed neutrons until they becomebombarded by high speed neutrons until they become
radioactive nucleiradioactive nuclei.
Ea!-#s o' radioisoto!#s:
a.
+.
c.
#$.) "adioisotope as tracers
Q+++ PnP 321&10311&
Q++ eP 0
1
32
16
32
1&
Q+++ ana 24111
0
23
11
Q++ e#a 0
1
24
12
24
11
Q+++ lnl 28131
0
2,
13
Q++ eil 0128142813
%"adio phosphorus&%"adio phosphorus&
%"adio sodium&%"adio sodium&
%"adio aluminum&%"adio aluminum&
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PHYSICS CHAPTER 15
27
Sic# radioisotoperadioisotope"as t"# same chemical properties as thesame chemical properties as the
stable isotopesstable isotopest"# t"#y ca +# us#d to trace the path madetrace the path madeby the stable isotopesby the stable isotopes.
Its #t"od :
A small amount of suitable radioisotopesmall amount of suitable radioisotopeis #it"#r
swallowedswallowed+y t"# !ati#t or in>ected into the body of thein>ected into the body of the
patientpatient. A't#r a w"i-# c#rtai !art o' t"# +ody wi-- "av# a+sor+#d
#it"#r a ora- aout* or a aout w"ic" is -ar,#r t"a
ora- or -#ss t"a ora- o' t"# radioisoto!#. A detectordetector
(suc" as eiger counter ,gamma cameraeiger counter ,gamma camera* #tc..) t"#
measures the count rate at the part of the bodymeasures the count rate at the part of the bodyconcernedconcerned.
It is us#d to investigate organsinvestigate organs i "ua +ody suc" as kid#y*
t"yroid ,-ad* "#art* +rai* ad #tc..
It a-so us#d to monitor the blood flowmonitor the blood flowad measure the bloodmeasure the blood
volumevolume.
#$.).) "adioisotope as tracers
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PHYSICS CHAPTER 15
28
A sa-- vo-u# o' a so-utio w"ic" cotai#d a radioactiv# isoto!#
o' sodiu "ad a activity o' 1%/// disit#,ratios !#r iut# w"#it was iD#ct#d ito t"# +-oodstr#a o' a !ati#t. A't#r 3/ "ours t"#
activity o' 1./ c3o' t"# +-ood was 'oud to +# /.5/ disit#,ratios
!#r iut#. I' t"# "a-'6-i'# o' t"# sodiu isoto!# is tak# as 15
"ours* #stiat# t"# vo-u# o' +-ood i t"# !ati#t.
Solution :Solution :T"# d#cay costat o' t"# sodiu isoto!# is
T"# activity o' sodiu a't#r 3/ " is ,iv# +y
Ea!-# 5 :
h30)"in12000h)1& 1
02/1 ===
tAT
2ln2/1 =T
2ln1& =
12 h1062*4 =
teAA = 0( ) ( )( )301062*4
2
12000= e
1
"in3000
=A
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PHYSICS CHAPTER 15
29
Solution :Solution :
I t"# dilutiondilutiontraci, #t"od* t"# activityactivityo' t"# sa!-#*AAis
proportionalproportionalto t"# volumevolumeo' t"# sa!-# !r#s#t* VV.
t"us t"# ratio o' activiti#s is ,iv# +y
T"#r#'or# t"# vo-u# o' t"# +-ood is
h30)"in12000h)1& 102/1 === tAT
VA11 kVA = 22 kVA =t"# ad
2
1
2
1
V
V
A
A=
2
1
3000
&*0
V=
32 c"6000=V
initialinitial finalfinal
%#$.8&%#$.8&
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PHYSICS CHAPTER 15
30
n medicinen medicine To d#stroy cac#r c#--s +y ,aa6ray 'ro a "i,"6activity
sourc# o' Co60/.
To tr#at d##!6-yi, tuors +y !-ati, radiu6%%0 or ca#siu6
13 isid# t"# +ody c-os# to t"# tuor.
n agriculturen agriculture
To #a+-# sci#tists to 'oru-at# '#rti-i#rs t"at wi-- icr#as# t"#
!roductio o' 'ood.
To d#v#-o! #w strais o' 'ood cro!s t"at ar# r#sistat to
dis#as#s* ,iv# "i," yi#-d ad ar# o' "i," 2ua-ity. To icr#as# t"# ti# 'or 'ood !r#s#rvatio.
#$.). !ther uses of radioisotope
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PHYSICS CHAPTER 15
31
n industryn industry
To #asur# t"# w#ar ad t#ar o' ac"i# !art ad t"#
#''#ctiv##ss o' -u+ricats.
To d#t#ct '-aws i ud#r,roud !i!#s #.,. !i!#s us# to carry
atura- !#tro-#u ,as.
To oitor t"# t"ick#ss o' #ta- s"##t duri, au'actur# +y
!assi, it +#tw## ,aa6ray ad a suita+-# d#t#ctor.n archaeology and geologyn archaeology and geology
To #stiat# t"# a,# o' a arc"a#o-o,ica- o+D#ct 'oud +y
r#'#rri, to car+o61 dati,.
To #stiat# t"# ,#o-o,ica- a,# o' a rock +y r#'#rri, to
!otassiu6/ dati,.
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PHYSICS CHAPTER 15
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Radioactiv# iodi# isoto!# o' "a-'6-i'# =./ days is us#d 'ort"# tr#at#t o' t"yroid ,-ad cac#r. A c#rtai sa!-# is r#2uir#d to
"av# a activity o' =./ 1/52 at t"# ti# it is iD#ct#d ito t"# !ati#t.
a. Ca-cu-at# t"# ass o' t"# iodi#6131 !r#s#t i t"# sa!-# to
!roduc# t"# r#2uir#d activity.
+. I' it tak#s % "ours to d#-iv#r t"# sa!-# to t"# "os!ita-* w"at
s"ou-d +# t"# iitia- ass o' t"# sa!-#
c. "at is t"# activity o' t"# sa!-# a't#r % "ours i t"# +ody o' t"#
!ati#t
(8iv# t"# Avo,adro costat* BA0./% 1/%3 o-1)
Ea!-# 0 :
( )131
&3
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PHYSICS CHAPTER 15
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Solution :Solution :
T"# d#cay costat o' t"# iodi# isoto!# is
a. 7ro t"# r#-atio +#tw## t"# d#cay rat# ad activity*
I' 0./% 1/%3 uc-#i o' 6131 "as a ass o' 131 , t"us
=./ 1/11 uc-#i o' 6131 "as a ass o'
( ) +)1091*66060240*8 &2/1 ==TB.100*8 &0 =A
2ln2/1 =T
2ln1091*6 & =
16 +1000*1 =
0
0
=dt
dNA
( ) 0
6& 1000*1100*8 N=00 NA =
nuclei100*8 110 =N
1311002*6
100*823
11
#10,4*1 10=
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PHYSICS CHAPTER 15
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Solution :Solution :
+. 8iv#
;#tN: ass o' 6131 a't#r % "ours
N0: iitia- ass o' 6131
y a!!-yi, t"# #!o#tia- -aw o' radioactiv# d#cay* t"us
c. 8iv#
T"# activity o' t"# sa!-# is
( ) +)1091*66060240*8 &2/1 ==TB.100*8 &0 =A
+108*64360024hr24 4===t#10,4*1 10=
t
eNN
= 0 ( )( )46 1064*81000*10
1010,4*1
= eN( ) ( )( )
46 1064*81000*110
0 10,4*1 = eN
#1090*1 10
0
=N+108*64360024hr24 4===t
teAA
= 0 ( ) ( )( )46 1064*81000*1&
100*8 = eA
B.1034*, &
=A
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PHYSICS CHAPTER 15
35
A arc"#o-o,ist o a di, 'ids a 'ra,#t o' a aci#t +ask#t
wov# 'ro ,rass. ;at#r* it is d#t#ri#d t"at t"# car+o61cot#t o' t"# ,rass i t"# +ask#t is
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PHYSICS CHAPTER 15
36
E#rcis# 15.1 :8iv#N0./% 1/
%3 o-1
1. ;ivi, wood tak#s i radioactiv# car+o61 'ro t"#atos!"#r# duri, t"# !roc#ss o' !"otosyt"#sis* t"# ratio o'car+o61 to car+o61% atos +#i, 1.%5 to 1/1% . "# t"#wood di#s t"# car+o61 d#cays* its "a-'6-i'# +#i, 50// y#ars. , o' car+o 'ro a !i#c# o' d#ad wood ,av# a tota- cout rat#o' %/./ disit#,ratios !#r iut#. t#ri# t"# a,# o' t"#
!i#c# o' wood.
A*S. :A*S. : ?
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PHYSICS CHAPTER 15
Good luck
7or
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