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CAREER POINT
PRACTICE PROBLEM SHEET
PHYSICS
Topic Nuclear Physics & Radioactivity-2
Q.1 The half life period of a radioactive elementXis same as the
mean life time of another radioactive element Y.
Initially both of them have the same number of atoms. Then -
(1)Xand Yhave the same decay rate initially (2)Xand Y decay at
the same rate always
(3) Ywill decay at a faster rate thanX (4)Xwill decay at a
faster rate than Y
Q.2 radioactive nuclide can decay simultaneously by two
different processes which have individual decay constants
1and 2respectively. The effective decay constant of the nuclide
is !iven by -
(1) " 21 (2)
1"
1
1
# 21
(3) "21 (1# 2) (4) " 1# 2
Q.3 radioactive sample has initial concentrationN$of nuclei
-
(1) The number of undecayed nuclei present in the sample decays
e%ponentially with time
(2) The activity (R) of the sample at any instant is directly
proportional to the number of undecayed nuclei
present in the sample at that time
(3) The number of decayed nuclei !rows linearly with time
(4) The number of decayed nuclei !rows e%ponentially with
time
Q.4 radioactive substance disinte!rates completely in 1$ days.
&uppose each day it disinte!rates at a rate which
is twice the rate of the precious day. The percenta!e of the
material left to be disinte!rated after passin! of '
days is (appro%) -
(1) 1$ (2) 2$ (3) 2 (4) $
Q.5 ssumin! that all laws of thermodynamics can be applied to a
nucleus the decay of a nucleus may be
re!arded as an -
(1) isothermal process (2) isobarric process (3) adiabatic
process (4) isochoric process
Q.6 AandBare isotopes.Band Care isobars. If dA dB and dcbe the
densities of nucleiABand Crespectively
then -
(1) dA* dB* dC (2) dA+ dB+ dc (3) dA" dB" dc (4) dA" dB+ dCQ.
radioactive nuclide is produced at the constant rate of nper second
(say by bombardin! a tar!et with neutrons).
The e%pected numberNof nuclei in e%istence tseconds after the
number isN$is !iven by
(1)N"N$e,t (2)N"
n#N$e
,t
(3)N"
n#
n
N ,$ e,t (4)N"
n#
+n
N$ e,t
here is the decay constant of the sample/
Q.! The percenta!e of 0uantity of a radioactive material that
remains after half lives will be -
(1) 31 (2) 3.12 (3) $.3 (4) 1
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PRE
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Q.# The masses of two radioactive substances are same and their
half lives are 1 year and 2 year respectively. The
ratio of their activities after si% year will be -
(1) 1 4 (2) 4 1 (3) 1 (4) 1
Q.1" In a cancer therapy unit patients are !iven treatment from
a certain radioactive source This source has a half-
life of 4 years. particular treatment re0uires 1$ minutes of
irradiation when the source is first used. 5ow
much time is re0uired for this treatment usin! the same source 2
years later 6
(1) 7 minutes (2) 1$ minutes (3) 14 minutes (4) 2$ minutes
Q.11 8adiation from a radioactive source enters an evacuated
re!ion in which there is a uniform ma!netic field
perpendicular to the plane of the dia!ram. This re!ion is
divided into two by a sheet of aluminum about 1
mm thic9. The curved hori:ontal path followed by the radiation
is shown in fi!. hich of the followin!
correctly describes the type of radiation and its point of
entry
type of radiation point of entry
(1) alpha x
(2) alpha y
(3) beta x
(4) beta y
Q.12 If 1$ of a radioactive substance decays in every years then
the percenta!e of the substance that will have
decayed in 2$ years will be -
(1) 4$ (2) $ (3) ;.; (4) 34.4
Q.13 t time t" $ some radioactive !as is in
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Q.14 =ranium ores contain one radium-22; atom for every 2. >
1$ ;uranium-23 atoms. ?alculate the half-life of
'2=23!iven that the half-life of 8a
22;is 1;$$ years (8a22;is a decay product of '2=
23) -
(1) 1.7 > 1$3years (2) 1;$$ >'2
23years (3) 4. > 1$'years (4) 1;$$ >
23
'2years
Q.15 sample of radioactive material contains 1$ 1atoms. The
half-life of the material is 2.$ days@ then the
activity of the sample is -
(1) 3. > 1$12A0 (2) 7 > 1$11A0 (3) 7 > 1$1;A0 (4) 3.
> 1$14A0
Q.16 radioactive sample with half-life 1 hour has > 1$ 1$
atoms at time t "$. The number of atoms decayin!
between t " 2 hrs and t " 4 hrs is-
(1) 4 > 1$1$ (2) 1. > 1$1$ (3) :ero (4) 2 > 1$1$
Q.1 &uppose the dau!hter nucleus in a nuclear decay is
itself radioactive. If dand m denote the decay constants
of dau!hter and mother nuclei andNdandNmthe numbers of dau!hter
and mother nuclei present at a time
then the number of dau!hter nuclei becomes constant when -
(1) mNm" dNd (2) mNd" dNm (3)Nm,Nd" m, d (4)Nm#Nd" m# d
ANSWERS$
1.%3x
;'3.$"
y1
y * %
&incex
dt
dN
, " xN
ndydt
dN
, " yN
ydt
dN
, >
xdt
dN
,
ecay rate of Y>ecay rate ofX.
2.%4 Brobability of distinct increases.
3.%1'2'4
N"N$e,t
N " Cumber of undecayed nuclei in the
sample at time t.
Total number of undecayed nuclei e0uals (N$,N)
(N$,N) "N$(1 , e,t)
hich is !rowin! e%ponentially with time.ctivityR" , N"
dt
dN
4.%4 Dn the last day we have 1$$ decay i.e. on
the ninth day $ decay must be there or
$ must be left.
5.%3 &ince decay is to be re!arded as a statistical
spontaneous process hence decay can be
re!arded as an diabatic process.
6.%3 &ince nuclear density is independent of mass
of nucleus hence all possess e0ual density.
.%3dt
dN" n , N
Aecause the population N is simultaneously
increasin! at rate n and decreasin! due to
decay at rate N.
N
NNn
dN
$
,"
t
dt
$
1 ln
Nn
Nn
,
, $" t
N"
n#
n
N ,$ e,t
Db
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$N
N> 1$$ " 32
1$$" 3.12.
!.%1 N1" C$ 1E;2
1
" ;$
2
N
!ain C2" C$ 2E;2
1" 3
$
2
N
ividin!2
1
N
N
" ;
3
2
2
"4
1
CowA" N"T
N;'3.$
2
1
A
A "
2
1
N
N
"
2
1
N
N
1
2
T
T
"4
1
>1
2 "
4
1.
#.%3 If C$is the initial particles of the radioactivesource
then
initial activity$
dtdN
" , C$
where C " C$e,t@ t in years.
"4
2ln
@ half-life " 4 years.
Cumber of radioactive particles needed forthe treatment is
C ";$243;(4
1$
$
dt
dN
";$243;(4
1$$
N
FFF(1)
Two years later the activity remained is
2
2
Ndt
dN =
" , C$ e,2
If minutes is needed for the same treatment then
C ";$243;(4
2
tdt
dN
;$243;(4
2
$
eNt
FF..(2)
i. e. t " 1$e2"2ln
2
1
1$e "21$ minute
" 14.1 minute
11.%1'4-rays are electroma!netic waves of which no
deflection is observed when a beam of -raysis allowed to pass
throu!h a ma!netic field.since the presence of ma!netic field
deflectsthe path of the radiation particularly near Gthe radiation
must either be -particles or -particles
12.%4 C"C$e,t
$N
N" e,t @
N
N$" e,t @ t " lo!e N
N$@
t "
1lo!e
N
N$
@ t lo!e N
N$
@
lo!e '$
1$$
2$ H lo!e N
N$
ividin!
2$
"
N
N$1$
1$
lo!
'$
1$$lo!
or lo!1$'
1$lo!4 1$
$ =N
N
or4
$
'
1$
=N
N
or
4
$ 1$
'
=N
N" $.;;1
Bercenta!e of substance that decays" (1,$.;;1) 1$$ " 34.3'
13.%2 The rate at which the atoms decays from theradioactive !as
is proportional to the umberof atoms present in the !as by the
e0uation
Ndt
dN=
where is the radioactive decay constant.rom which we obtainC "
C$e
,t
where C$is the initial number of atoms in the!as at t " $It is a
strai!ht line of ne!ative !radient withma!nitude l when ln C is
plotted a!ainst t.Thus from t " $ to T the lo!arithmic of
number of atoms lnC decreases uniformly at
the rate of for the time period from t " $ to
t " T. hen more of the same !as is in 2. > 1$;
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" 4.4 > 1$'years J,
4. > 1$'years
15.%1 NT
A = ;'3.$
16.%2 T " 1 5r C$" > 1$1$atoms
C1" TEt$
12
C
" 1E2
1$
2
1$" 4
1$ 1$
" 2 >
1$1$
C2" TEt$
22
C
" 1E4
1$
2
1$" 1;
> 1$1$" $. >
1$1$
C " C1, C2" (2 , $.) > 1$1$" 1. > 1$1$
1.%1 The number of mother nuclei decayin! in ashort time
interval dt is "Nmmdt. Aut deathof a mother nucleus implies the
birth of adauther nucleus.The number of dau!hter nuclei decayin!
inthe same time interval is "Ndddt.Nmmdt"NdddtorNmm"Ndd
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