CHAPTER -13 NUCLEI

Before the neutrino hypothesis, the beta decay process was
throught to be the transition,
n → p + e
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.

Deuteron is a bound state of a neutron and a proton with a
binding energy B = 2.2 MeV. A γ -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 γ-ray.
If E = B, show that this cannot happen. Hence calculate how
much bigger than B must E be for such a process to happen.

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 23
11 Na ? (b) Which
nuclide out of the two mirror isobars have greater binding energy
and why?

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 of 14C is
5760 years.

Consider a radioactive nucleus A which decays to a stable nucleus
C through the following sequence:
A → B → C
Here B is an intermediate nuclei 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.

Why do stable nuclei never have more protons than neutrons?

In pair annihilation, an electron and a positron destroy each other
to produce gamma radiation. How is the momentum conserved?

Which one of the following cannot emit radiation and why?
Excited nucleus, excited electron.

Draw a graph showing the variation of decay rate with number
of active nuclei.

He2 and 3
He1 nuclei have the same mass number. Do they have
the same binding energy?

The neutron separation energy is defined as the energy required to remove a neutron from the nucleus. Obtain the neutron separation energies of the nuclei and from the following data:

= 39.962591 u

) = 40.962278 u

= 25.986895 u

) = 26.981541 u

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 (23.98504u), (24.98584u) and

 (25.98259u). The natural abundance of is 78.99% by mass. Calculate the abundances of other two isotopes.

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.

From the relation R = R₀A¹/³, where R₀is a constant and A is the mass number of a nucleus, show that the nuclear matter density is nearly constant (i.e. independent of A).

Calculate the height of the potential barrier for a head on collision of two deuterons. (Hint: The height of the potential barrier is given by the Coulomb repulsion between the two deuterons when they just touch each other. Assume that they can be taken as hard spheres of radius 2.0 fm.)

How long can an electric lamp of 100W be kept glowing by fusion of 2.0 kg of deuterium? Take the fusion reaction as

A 1000 MW fission reactor consumes half of its fuel in 5.00 y. How much did it contain initially? Assume that the reactor operates 80% of the time, that all the energy generated arises from the fission of and that this nuclide is consumed only by the fission process.

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?

The Q value of a nuclear reaction A + b Ã¢â€ ’ C + d is defined by

Q = [ mA+ mb - mC - md]c2 where the masses refer to the respective nuclei. Determine from the given data the Q-value of the following reactions and state whether the reactions are exothermic or endothermic.

(i) 

(ii) 

Atomic masses are given to be

The nucleus decays byemission. Write down the decay equation and determine the maximum kinetic energy of the electrons emitted. Given that:

= 22.994466 u

= 22.989770 u.

The radionuclide 11C 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

Find the Q-value and the kinetic energy of the emitted α-particle in the α-decay of (a) and (b).

Given = 226.02540 u, = 222.01750 u,

= 220.01137 u, = 216.00189 u.

Obtain approximately the ratio of the nuclear radii of the gold isotope and the silver isotope.

  The half-life ofis 28 years. What is the disintegration rate of 15 mg of this isotope?

Obtain the amount ofnecessary to provide a radioactive source of 8.0 mCi strength. The half-life ofis 5.3 years.

 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 Mohenjodaro gives an activity of 9 decays per minute per gram of carbon. Estimate the approximate age of the Indus-Valley civilisation.

A radioactive isotope has a half-life of T years. How long will it take the activity to reduce to a) 3.125%, b) 1% of its original value?

Write nuclear reaction equations for

(i) α-decay of  (ii) α-decay of 

(iii) ÃŽÂ² - -decay of  (iv) ÃŽÂ² - -decay of 

(v) ÃŽÂ²+-decay of  (vi) ÃŽÂ²+-decay of 

(vii) Electron capture of 

 A given coin has a mass of 3.0 g. Calculate the nuclear energy that would be required to separate all the neutrons and protons from each other. For simplicity assume that the coin is entirely made ofatoms (of mass 62.92960 u).

Obtain the binding energy of the nuclei  and in units of MeV from the following data:

 = 55.934939 u = 208.980388 u

Obtain the binding energy (in MeV) of a nitrogen nucleus, given =14.00307 u

(a) Two stable isotopes of lithium  and have respective abundances of 7.5% and 92.5%. These isotopes have masses 6.01512 u and 7.01600 u, respectively. Find the atomic mass of lithium.

(b) Boron has two stable isotopes, and. Their respective masses are 10.01294 u and 11.00931 u, and the atomic mass of boron is 10.811 u. Find the abundances of  and .

The three stable isotopes of neon: and have respective abundances of 90.51%, 0.27% and 9.22%. The atomic masses of the three isotopes are 19.99 u, 20.99 u and 21.99 u, respectively. Obtain the average atomic mass of neon.

(a) Two stable isotopes of lithium  and have respective abundances of 7.5% and 92.5%. These isotopes have masses 6.01512 u and 7.01600 u, respectively. Find the atomic mass of lithium.

(b) Boron has two stable isotopes, and. Their respective masses are 10.01294 u and 11.00931 u, and the atomic mass of boron is 10.811 u. Find the abundances of  and .