# NCERT Solutions Class 12 Physics Chapter-13 (Nuclei)

NCERT Solutions Class 12 Physics from class 12th Students will get the answers of Chapter-13 (Nuclei) This chapter will help you to learn the basics and you should expect at least one question in your exam from this chapter.
We have given the answers of all the questions of NCERT Board Physics Textbook in very easy language, which will be very easy for the students to understand and remember so that you can pass with good marks in your examination.

Class 12 Physics

Chapter-13 (Nuclei)

Questions and answers given in practice

Chapter-13 (Nuclei)

Question 1.

(a) Two stable isotopes of lithiu 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

(a) Atomic weight of lithium

Question 2.

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.

Question 3.
Obtain the binding energy of a nitrogen nucleus
() from the following data :

mH = 1.00783 u
mn = 1.00867 u
mn = 14.00307 u

Question 4.
Obtain the binding energy of the nucle
i and

in units of from the following data:

mH =1007825u

mn =1008665u

()= 55.934939 u

m ()

Which nucleus has greater binding energy per nucleon?

Question 5.
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 o
f  atoms (of mass 62.92960 u). The masses of proton and neutron are 1.00783 u and 1.00867 u, respectively.

Question 6.
Write nuclear equations for :
(a) the α-decay o
f
(b) the β-decay o
f
(c) the β+-decay o
f

Question 7.
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 ?

Question 8.
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 radioactiv
e 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 146C , 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.

Half-life formula is the time required for the amount of something to fall to half its initial value.

Question 9.
Obtain the amount
of   necessary to provide a radioactive source of 8.0 mCi strength. The half­ life of   is 5.3 years.

Question 10.
The half-life
of   is 28 years. What is the disintegration rate of 15 mg of this isotope?

Question 11.
Obtain approximately the ratio of the nuclear radii of the gold isot
ope  and silver isotope .

Question 12.

Question 13.

Here mN stands for the nuclear mass of the element or particle. In order to express the Q value in terms of the atomic masses, 6 me mass has to be subtracted from the atomic mass o
f and 5 me mass has to be

Question 14.
The nucleu
decays by β~ emission. Write down the p-decay equation and determine the maximum kinetic energy of the electrons emitted. Given that:

m() = 22.994466 u

m() = 22.989770 u.

Question 15.
The Q value of a nuclear reaction A + b ⇒ C + d is defined by [Q = mA + mb-mc– md] cwhere the masses refer to nuclear rest masses. Determine from the given data whether the following reactions are exothermic or endothermic.

Question 16.
Suppose, we think of fission of
nucleus into two equal fragments, if   . Is the fission energetically possible ? Argue by working out Q of the process. Given, m (  ) = 55.93494 u and m)= 27.98191

Question 17.
The fission properties o
f   are very similar to those o . 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 ?

Question 18.
A 1000 MW fission reactor consumes half of its fuel in 5.00 y. How muc
h
23592u did it contain initially ? Assume that all the energy generated arises from the fission o
f   and that this nuclide is consumed by the fission process.

Question 19.
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

Question 20.
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.

The initial mechanical energy E of the two deutrons before collision is given by
E = 2 K.E.

Question 21.
From the relation R = RA1/3, where R 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)

Question 22.
For the β+ (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 β+ emission is energetically allowed, electron capture is necessarily allowed but not vice-versa

Question 23.
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 ar
2412Mg (23.98504u), ? (24.98584) and (25.98259u). The natural abundance of  is 78.99% by mass. Calculate the abundances of the other two isotopes.

Question 24.
The neutron separation energy is defined as the energy required to remove a neutron from the nucleus. Obtain the neutron separation energies of the nucle
i and from the following data :

Question 25.

Question 26.
Under certain circumstances, a nucleus can decay by emitting a particle more massive than an α-particle. Consider the following decay processes :

(a) Calculate the Q values for these decays and determine that both are energetically possible.
(b) The Coulomb barrier height for α-particle

Question 27.
Consider the fission o
f 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

Question 28.
Consider the D-T reaction (deuterium-tritium-fusion) given in eqn. :

(b) Consider the radius of both deuterium and tritium to be approximately 1.5 fm. What is the kinetic energy needed to overcome the Coulomb repulsion? To what temperature must the gases be heated to initiate the reaction?
From the equation given in the question,

mN refers to the nuclear mass of the element given in the brackets and mn = mass of the neutron. If in represents the atomic mass, then

Question 29.
Obtain the maximum kinetic energy of p-particles and the radiation frequencies to y decay in the following decay scheme. You are given that
m (198Au) = 197.968233 u
m (198Hg) = 197.966760 u

The total energy released for the transformation o
f to can be found by considering the energies of ϒ-rays. We first find the frequencies of the ϒ-rays emitted.

Question 30.

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 235U in a fission reactor.