CBSE Class 12 Physics VBQs Nuclei

QUESTIONS & ANSWERS:

Question. Why is the mass of a nucleus always less than the sum of the masses of its constituents?
Answer. The difference in masses of the constituents of the nucleus and the nucleus is known as mass defect,
This mass defect is converted into equivalent energy and released as binding energy when the nucleus is formed.

Question. Write the relation connecting the radius R, of nucleus and its mass number A.
Answer. Nuclear radius, R = R₀ A^1/3 where R0 = 1.1 x 10^-15m.

Question. Name the reaction responsible for energy production in the sun.
Answer. Nuclear fusion.

Question. What is the nuclear radius of 125Fe, if that of 27Al is 3.6 fermi?
Answer. Hint: R = R₀ A^1/3
R_Fe/R_Al = 5/3,
R_Fe = 6.0 fermi.

Question. Two nuclei have mass numbers in the ratio 27 : 125. What is the ratio of their nuclear radii?
Answer. R₁/R₂ = {A₁/A₂}^1/3
= {27/125}^1/3 = 3/5 = 3 : 5.

MCQs

Question. The ratio of the volume of an atom to the volume of its nucleus is of the order of:
(a) 10
(b) 105
(c) 1010
(d) 1015
Answer. D

Question. Binding energy of a nucleus is of the order of:
(a) Electron volt (eV)
(b) Kilo electron volt (keV)
(c) Mega electron volt(MeV)
(d) joule (J)
Answer. C

Question. As the mass number of a nucleus increases, the binding energy per nucleon:
(a) Goes on increasing
(b) Goes on decreasing
(c ) Remains the same
(d) First increases, then decreases.
Answer. D

Question. The stability of a nucleus is decided by its:
(a) Binding energy
(b) Binding energy/nucleon
(c) Number of protons
(d) Number of nucleons
Answer. B

Question. The curve of binding energy per nucleon against mass number has a sharp peak for helium nucleus. This means that helium nucleus:
(a) Is very stable
(b) Is radioactive
(c) Is easily fissionable
(d) None of these.
Answer. A

Question. The radius of a nucleus is
(a) directly proportional to its mass number
(b) inversely proportional to its atomic weight
(c) directly proportional to the cube root of its mass number
(d) None of these
Answer. C

Question. A neutron can cause fission in
(a) Hydrogen
(b) Uranium – 235
(c) Thorium
(d)Uranium – 238
Answer. B

Question. One milligram of matter converted into energy, will give
(a) 9 J
(b) 9 x 10³ J
(c) 9 x 10⁵ J
(d) 9 x 10¹⁰
Answer. D

Question. The mass density of a nucleus varies with mass number A as
(a) A²
(b) A
(c) Constant
(d) 1/ A
Answer. C

Question. Fusion reaction takes place at high temperature because
(a) Nuclei break up at high temperature
(b)Atoms gets ionised at high temperature
(c) Kinetic energy is high enough to overcome the coulomb repulsion between nuclei
(d)Molecules break up at high temperature.
Answer. C

ASSERTION REASON TYPE QUESTIONS
Given below two statements labelled as Assertion (A) and Reason (R). Select the most appropriate answer from the following:
(a) Both A and R are correct and R is the correct explanation of A
(b)Both A and R are correct and R is the correct explanation of A
(c) A is true but R is false
(d)Both A and R are false

Question. Assertion: The nuclear force becomes weak if the nucleus contains too many protons compared to neutrons
Reason: The electrostatic forces weaken the nuclear force.
Answer. C

Question. Assertion: Mass is not conserved, but mass and energy as a single entity called mass- energy.
Reason: Mass and energy are inter-convertible in accordance with Einstein’s relation, E = mc²
Answer. A

Question. Assertion: Two protons can attract each other.
Reason: The distance between the protons within the nucleus is about 10^-15 m.
Answer. A

SA (2 marks)

Question. Imagine the fission of a ⁵⁶₂₆𝐹𝑒 into two equal fragments of 𝐴𝑙1328 nucleus. Is the fission energetically possible? Justify your answer by working out Q value of the process.
Given: m {⁵⁶₂₆𝐹𝑒}= 55.93494u, m {²⁸₁₃𝐴𝑙} = 27.98191u.
Answer. Mass Difference = 55.93494 – 2 x 27.98191
= -0.02888u.
Fission not possible.

Question. Why do stable nuclei never have more protons than neutrons?
Answer. Protons are positively charged and repel one another electrically.
This repulsion becomes so great in nuclei with more than 10 protons or so, that an excess of neutrons which produce only attractive forces, is required for stability.

Question. If 200 MeV energy is released in the fission of one U²³⁵ nucleus, how many fissions must occur per second to produce a power of 2KW?
Answer. Energy released in fission of U235 nucleus = 200 MeV
= 3.2 x 10^-11J
If the number of fissions required per second to produce a power of 2 kW is n, then
3.2 x 10^-11 x n = 2 x 1000
n = 2 x 1000 / 3.2 x 10^-11 = 6.25 x 10¹³.

Question. (a) Write two characteristic properties of nuclear force.
(b) How does one explain the release of energy in the processes of nuclear fission and nuclear fusion?
Answer. (a) Characteristics of nuclear forces (Any two)
(i)Nuclear forces are attractive in nature: - The magnitude which depends upon inter nucleon distance is of very high order.
(iii) Nuclear forces are charge independent: - Nature of force remains the same whether we consider force between two protons, between two neutrons or between a proton and a neutron.
(iv) These are short range forces: - Nuclear forces operate between two nucleons situated in close neighbourhood only.
(v) Nuclear forces decrease very quickly with distance between two nucleons: - Their rate of decrease is much rapid than that of inverse square law forces.
(vi) Nuclear forces are spin dependent: - Nucleons having parallel spin are more strongly bound to each other than those having anti-parallel spin.
(b) The breaking of a heavy nucleus into smaller nuclei is called nuclear fission while the combining of two light nuclei to form a heavy nucleus is called nuclear fusion.
In both the processes, the binding energy of the daughter nuclei is more than that of the parent nuclei.
The difference in binding energy is released in the form of energy. In both processes, some mass gets converted into energy.

Case Study

1. NUCLEAR FORCE
Neutrons and protons are identical particle in the sense that their masses are nearly the same and the force, called nuclear force, does into distinguish them. Nuclear force is the strongest force. Stability of nucleus is determined by the neutron Proton ratio or mass defect or packing fraction. Shape of nucleus is calculated by quadrupole moment and the spin of nucleus depends on even or odd mass number. Volume of nucleus depends on the mass number. Whole mass of the atom (nearly 99%)is centred at the nucleus.

Question. The incorrect statement about the nuclear force is
(a) Charge independent
(b) Short range force
(c) Non conservative force
(d) Obeys inverse square law
Answer. A

Question. The range of nuclear force is the order of
(a) 2 x10 ^-10 m
(b) 1.5 x10^-20 m
(c) 1.2 x10 ^{– 4}m
(d) 1.4 x10 ^{– 15} m
Answer. D

Question. Density of a nucleus
(a) Increases with mass number
(b) Decreases with mass number
(c) Constant for any nucleus
(d) low density for small nuclei and large for heavy nuclei
Answer. C

Question. 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.
Answer. B

2. BINDING ENERGY OF A NUCLEUS
An atomic nucleus is composed of protons and neutrons. The measurements using mass spectrometer have revealed that the mass of a stable nucleus is always less than the sum of the masses of its constituent protons and neutrons. The difference in the mass of a nucleus and its constituents is called mass defect, Δm = Zmp + (A – Z)mn – M. Using Einstein’s mass energy relation, we express this mass difference in terms of energy as ΔEb = mc2. This energy ΔEb is called the binding energy of the nucleus. This energy represents the surplus energy which the nucleons give upby virtue of their mutual attraction when they become bound together to form a nucleus. The value of binding energy per nucleon of a nucleus gives a measure of the stability of that nucleus. Greater is the binding energy per nucleon of a nucleus, more stable is the nucleus. In the mass number range A = 30 to 170, the binding energy per nucleon is nearly constant, about 8 MeV/nucleon.

Question. If the number of nucleons increases, then binding energy per nucleon of the nucleus
(a) First increases and then decreases with mass number
(b) Continuously increases with mass number
(c) Continuously decreases with mass number
(d) Remains constant with mass number.
Answer. A

Question. The average binding energy per nucleon is maximum for the nucleus
(a) ⁴₂𝐻𝑒
(b) ¹⁶₈𝑂
(c) ⁵⁶₂₆ 𝐹𝑒
(d) ²³⁸₉₂𝑈
Answer. C

Question. The curve of binding energy per nucleon as a function of a atomic mass number has a sharp peak for helium nucleus. This implies that helium nucleus
(a) Can easily be broken up
(b) Is very stable
(c) Can be used as fissionable material
(d) Is radioactive
Answer. B

Question. If mo is the mass of isotope 𝑂816, mp and mn are the masses of a proton and neutron respectively, the nuclear binding energy of the isotope is
(a) (m_o - 16 m_n)c²
(b) (m_o - 8m_p)c²
(c) (8m_p + 8 m_n - m_o)c²
(d) m_oc²
Answer. C

Question. The binding energy per nucleon is almost same for many nuclei. It indicates that the nuclear forces are:
(a) Attractive
(b) short-range
(c) charge-independent
(d) saturated
Answer. D

3. NUCLEAR FISSION
In a single uranium fission about 0.9 x 235 MeV (≈ 200MeV) of energy is liberated. If each nucleus of about 50 kg of U235 undergoes fission the amount of energy involved is about 4 x 1015J. This energy is equivalent to about 20000 tons of TNT, enough for a super explosion. Uncontrolled release of large nuclear energy is called an atomic explosion. On August 6, 1945 an atomic device was used in warfare for the first time. The US dropped an atom bomb on Hiroshima, Japan. The explosion was equivalent to 20000 tons of TNT. Instantly the radioactive products devastated 10 sq km of the city which had 343000 inhabitants. Of this number 66000 were killed and 69000 were injured, more than 67% of the city structures were destroyed.

Question. When ₉₂U²³⁵ undergoes fission, about 0.1% of the original mass is converted into energy. The energy released when 1 kg of ₉₂U²³⁵ undergoes fission is
(a) 8.2 x 10¹¹ J
(b) 8.2 x 10¹³ J
(c) 8.2x 10¹⁵ J
(d) 8.2 x 10¹⁸ J
Answer. B

Question. In any fission process, ratio of mass of daughter nucleus to mass of parent nucleus is
(a) Less than 1
(b) Greater than 1
(c) Equal to 1
(d) Depends on the mass of parent nucleus
Answer. A

Question. A nuclear fission is said to be critical when multiplication factor or K
(a) K = 1
(b) K > 1
(c) K < 1
(d) K = 0
Answer. A

Question. On an average, the number of neutrons and the energy of a neutron released per fission of a uranium atom are respectively
(a) 2.5 and 2 keV
(b) 3 and 1 keV
(c) 2.5 and 2 MeV
(d) 2 and 2 keV
Answer. C