-
(a) Two stable
isotopes of lithium
and
have
respective abundance of 7.5% and 92.5%. These isotopes have masses 6-01512 u
and 7-01600 u respectively.
Find the
atomic weight of lithium.
(b)
Boron has two stable isotopes
and
. Their
respective masses are 10-01294 u and 11-00931 u and the atomic weight of boron
is 10-811 u. Find the abundances of
and
.
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The three stable
isotopes of neon :
and
have
respective abundance of 90-51%, 0-27% and 9-22%.
The
atomic masses of three isotopes are 19-99 u, 20-99 u and 21-99 u, respectively.
Obtain the
average atomic mass of neon.
-
Obtain the
binding energy of a nitrogen
nucleus
from
the following data :
Give your answer
in Me V.
-
Obtain the
binding energy of the nuclei
and
in
units of MeV from the following data :
Which
nucleus has greater binding energy per nucleon ?
-
Write nuclear
equations for :
(a) the
decay
of
(b) the
-decay
of
(c) the
-decay
of *^C
-
Write nuclear
equations for :
(a) the
decay
of
(b) the
-decay
of
(c) the
-decay
of *^C
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A radioactive isotope has a half-life of T years. After how much time is its activity reduced to 3-125% of its original activity
(b) 1% of original value ?
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The normal
activity of living carbon- containing matter is found to be about 15 decays per
minute for every gram of carbon.
This activity
arises from the small proportion of radioactive
present
with the stable carbon isotope
. When the organism is
dead, its interaction with the atmosphere (which maintains the above equilibrium
activity) ceases and its activity begins to drop. From the known half-life (5730
years) of
, and the measured activity,
the age of the specimen can be approximately estimated. This is the principle of
dating
used in archaeology. Suppose a specimen from Mohenjo-Daro gives an activity of
9 decays per minute per gram of carbon. Estimate the approximate age of the
Indus-Valley civilisation.
-
Obtain the amount
of
necessary to provide a
radioactive source of 8-0 mCi strength. The half-life of
is
5.3 years.
-
Obtain the amount
of
necessary to provide a
radioactive source of 8-0 mCi strength. The half-life of
is
5.3 years.
-
Obtain approximately
the ratio of the nuclear radii of the gold isotope
and silver isotope
Ag.
-
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The radionuclide
decays
according to
The
maximum energy of the emitted positron is 0-960 MeV.
Given the
mass values :
Calculate Q and
compare it with the maximum energy of the positron emitted.
-
The nucleus
decays
by
emission.
Write
down the
decay equation and determine
the maximum kinetic energy of the electrons emitted. Given that:
-
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Suppose, we think
of fission of a
nucleus into two
equal fragments,
. Is the fission
energetically possible ? Argue by working out Q. of the process. Given,
and
-
The fission
properties of
are very similar to
those of
The average energy
released per fission is 180 MeV.
How much energy,
in MeV, is released if all the atoms in 1 kg of pure
undergo fission
?
-
A 1000 MW fission
reactor consumes half of its fuel in 5-00 y. How much
did
it contain initially ? Assume that all the energy generated arises from the
fission of
and that this nuclide
is consumed by the fission process.
-
How long an
electric lamp of 100 W can be kept glowing by fusion of 2.0 kg of deuterium ?
The fusion reaction can be taken as
.
-
Calculate the height of Coulomb barrier for the head-on collision of two deuterons.
The effective radius of deuteron can be taken to be 2.0 fm.
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From the relation
where
is
a constant and A is the mass number of a nucleus, show that nuclear matter
density is nearly constant (i.e. independent of A).
-
For the
(positron)
emission from a nucleus, there is another competing process known as electron
capture (electron from an inner orbit, say, the K- shell, is captured by the
nucleus and a neutrino is emitted).
Show that if
emission
is energetically allowed, electron capture is necessarily allowed but not
vice-versa.
-
In a Periodic
Table the average atomic mass of magnesium is given as 24.312 u.
The average value
is based on their relative natural abundance on Earth. The three isotopes and
their masses are
and
(25.98259
u). The natural abundance of
is 78.99% by mass.
Calculate the abundances of the other two isotopes.
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A source contains
two phosphorus radionuclide?s
and
Initially,
10% of the decays come from
How long one must
wait until 90% do so ?
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Consider the fission of
by fast neutrons. In one fission event, no neutrons are emitted and the final stable end products, after the beta-decay of the primary fragments, are
and
Calculate Q for this fission process. The relevant atomic and particle masses are :
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Consider the D-T reaction (deuterium- tritium-fusion) given in eqn :
(a) Calculate the energy released in MeV in this reaction from the data :
(b) Consider the radius of both deuterium and tritium to be approximately 1-5 fin.
What is the kinetic energy needed to overcome the Coulomb repulsion ? To what temperature must the gases be heated to initiate the reaction ?
-
Obtain the
maximum kinetic energy of
particles, and the
radiation frequencies to y decays in the following decay scheme.
You are
given that
-
Calculate and
compare the energy released by (a) fusion of 1.0 kg of hydrogen deep within the
sun and (b) the fission of 1.0 kg of
in a fission
reactor.
-
Suppose India had a
target of producing by 2020 AD, 200,000 MW of electric power, ten percent of
which was to be obtained from nuclear power plant. Suppose we are given that, on
an average, the efficiency of utilisation (i.e., conversion to electric energy)
of thermal energy produced in a reactor was 25%. How much amount of fissionable
uranium did our country need per year by 2000 ? Take the heat energy per
fission of
to be about 200 MeV.
Avogadro's number
.
-
question_answer32)
Suppose we consider
a large number of containers each containing initially 10000 atoms of a
radioactive material with a half life of 1 year. After 1 year.
(a) all the
containers will have 5000 atoms of the material
(b) all the containers will contain the same number of
atoms of the material but that number will only be approximately 5000
(c) the containers will in general have different numbers
of the atoms of the material but their average will be close to 5000
(d) none of
the containers can have more than 5000 atoms
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question_answer33)
The gravitational
force between a H-atom and another particle of mass m will be given by Newton's
law:
where r is in km and
(a) 
(b) 
(c) M is not related to the mass of the hydrogen atom
(d) 
magnitude
of the potential energy of electron
in
the H-atom)
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question_answer34)
When a nucleus in
an atom undergoes a radioactive decay, the electronic energy levels of the atom
(a) do not
change for any type of radioactivity
(b)
change for a and p radioactivity but not for
-radioactivity
(c)
change for 
-radioactivity but not for others
(d) change
for 
-radioactivity but not for others
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question_answer35)
and 
denote
the atomic masses of the parent and the daughter nuclei respectively in a
radioactive decay. The Q -value for a -
decay is Q1 and that for a 
decay
is Q2. If me, denotes the mass of an electron, then which
of the following statements is correct?
(a)
and 
(b)
and
(c)
and
(d)
and
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question_answer36)
Tritium is an
isotope of hydrogen whose nucleus Triton contains 2 neutrons and 1 proton. Free
neutrons decay into 
If one of the
neutrons in Triton decays, it would transform into He3 nucleus. This
does not happen. This is because
(a) Triton
energy is less than that of a He3 nucleus
(b)
the electron created in the beta decay process can not remain in the nucleus
(c)
both the neutrons in triton have to decay simultaneously resulting in a nucleus
with 3 protons, which is not a He3 nucleus
(d)
because free neutrons decay due to external perturbations which is absent in a
triton nucleus
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question_answer37)
Heavy stable nuclei
have more neutrons than protons. This is because of the fact that
(a)
neutrons are heavier than protons
(b)
electrostatic force between protons are repulsive
(c)
neutrons decay into protons through beta decay
(d)
nuclear forces between neutrons are weaker
than
that between protons
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question_answer38)
In a nuclear reactor,
moderators slow down the neutrons which come out in a fission process. The moderator
used have light nuclei. Heavy nuclei will not serve the purpose
because
(a)
they will break up
(b)
elastic collision of neutrons with heavy nuclei will not slow them down
(c)
the net weight of the reactor would be unbearably high
(d)
substances with heavy nuclei do not occur in liquid or gaseous state at room
temperature
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question_answer39)
Fusion processes,
like combining two deuterons to form a He nucleus are impossible at
ordinary temperatures and pressure. The reasons for this can be traced to the
fact:
(a) nuclear forces have short range
(b) nuclei are positively charged
(c) the original nuclei must be completely ionized before
fusion can take place
(d) the original nuclei must first break up before combining
with each other
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question_answer40)
Samples of two
radioactive nuclides A and B are taken. 
and
are the disintegration constants
of A and B respectively. In which of the following cases, the two samples can
simultaeously have the same decay rate at any time?
(a) initial
rate of decay of A is twice the initial
rate
of decay of B and =
(b)
Initial rate of decay of A is twice the initial
rate
of decay of B and 
(c)
Initial rate of decay of B is twice the initial
rate
of decay of A and
(d)
Initial rate of decay of 5 is same as the rate of decay of A at t =2h and
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question_answer41)
The variation of
decay rate of two radioactive samples A and B with time is shown in Fig. 8(EP).l1.
Which of the
following statements are true?
a)
Decay constant of A is greater than that of B, hence A always decays faster than
B
b)
Decay constant of B is greater than that of A but its decay rate is always
smaller than that
of A
c)
Decay constant of A is greater than that of B but it does not always decay
faster than B
(d)
Decay constant of B is smaller than that of Abut still its decay rate becomes
equal to that of A at a later instant
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question_answer42)
2He3
and 
nuclei have the same mass
numbers. Do they have the same binding energy?
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question_answer43)
Draw a graph
showing the variation of decay rate with number of active nuclei.
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question_answer44)
Which sample, A or
B shown in Fig. 8(EP).3 has shorter mean-life?
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question_answer45)
Which one of the
following can not emit radiation and why? Excited nucleus, excited electron.
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question_answer46)
In pair
annihilation, an electron and a positron destory each other to produce gamma
radiation. How is the momentum conserved?
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question_answer47)
Why do stable
nuclei never have more protons than neutrons?
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question_answer48)
Consider a radioactive
nucleus A which decays to a stable nucleus C through the following sequence: A ® B® C
Here, B is an intermediate nucleus which is also radioactive. Considering that
there are N0 atoms of A initially, plot the graph showing the
variation of number of atoms of A and B versus time.
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question_answer49)
A piece of wood
from the ruins of an ancient building was found to have a 14C
activity of 12 disintegrations per minute per gram of its carbon content. The 14C
activity of the living wood is 16 disintegrations per minute per gram. How long
ago did the tree, from which the wooden sample came, die? Given half-life 14C
is 5760 year.
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question_answer50)
Are the nucleons
fundamental particles, or do they consist of still smaller parts? One way to find
out is to probe a nucleon just as Rutherford probed an atom. What should be the
kinetic energy of an electron for it to be able to probe a nucleon? Assume the
diameter of a nucleon to be approximtely 
m.
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question_answer51)
A nuclide 1 is said
to be the mirror isobar of nuclide 2 if Z1 = N2 and Z2
= N1. (a) What nuclide is a mirror isobar of? 
Na? (b) Which nuclide out of the
two mirror isobars has greater binding energy and why?
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question_answer52)
Sometimes a
radioactive nucleus decays into a nucleus which itself is radioactive. An
example is :
Assume that we start with 1000
38S nuclei at time t=0. The number of 38CI is of count zero at
t= 0 and will again be zero at 
, At what value
of t, would the number of counts be a maximum?
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question_answer53)
Deuteron is a bound
state of a neutron and a proton with a binding energy B = 2.2 M
. A -ray
of energy E is aimed at a deuteron nucleus to try to break it into a (neutron +
proton) such that the n and p move in the direction of the Incident -ray. If E=B, show that this can
not happen. Hence, calculate how much bigger than B must E be for such a
process to happen.
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question_answer54)
The deuteron is bound
by nuclear forces just as H-atom is made up of p and e bound by electrostatic
forces. If we consider the force between neutron and proton in deuteron as
given in the form of a Coulomb potential but with an effective charge e': 
estimate the value of (e'/e) given
that the binding energy of a deuteron is 2.2 M.
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question_answer55)
Before the neutrino
hypothesis, the beta process was thought to be the transition, 
If this was true, show that if
the neutron was at rest, the proton and electron would emerge with fixed energies
and calculate them. Experimentally, the electron energy was found to have a
large range.
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question_answer56)
The activity R of
an unkown radioactive nuclide is measured at hourly intervals. The results
found are tabulated as follows :
|
t(h)
|
0
|
1
|
2
|
3
|
4
|
|
100
|
35.36
|
12.51
|
4.42
|
1.56
|
(i) Plot the graph of R versus ( and calculate half-life
from the graph.
(ii)Plot the graph of In
versus
(and obtain the value of half-life from the graph.
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question_answer57)
Nuclei
with magic no. of proton Z = 2, 8,20,28,50,52 and magic no. of neutrons N=2,8,
20,28,50, 82 and 126 are found to be very stable, (i) Verify this by
calculating the proton separation energy Sp for 120Sn (Z = 50) and 121Sb
= (Z = 51).The proton separation energy for a nuclide is the minimum energy required
to separate the least tightly bound proton from a nucleus of that nuclide. It
is given by
(ii)
What does the existence of magic number indicate?
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particle in the
a-decay of (a) 
Ra (b) 
Rn
. Given, 
is defined
by
where the
masses refer to nuclear rest masses. Determine from the given data whether the
following reactions are exothermic or endothermic.
(i) 
(ii) 
Atomic
masses are given to be
and
from the following
data :
(a) Calculate
the Q values for these decays and determine that both are energetically possible.
(b)
The Coulomb barrier height for 
particle emission is
30.0 MeV. What is the barrier height for 
? The required data is
