Assertion (A) : Nuclear forces are always attractive.
Reason (R) : The nuclear force between protons and neutrons in a nucleus is a weak force.
CBSE CLASS 12 • PHYSICS • CHAPTER 13
Nuclei
51 distinct questions across 82 board paper set appearances (2022–2026).
Explain the terms mass defect and binding energy. How are they related?
The radius of a nucleus of mass number $125$ is
(A) $6\cdot 0\text{ fm}$
(B) $30\text{ fm}$
(C) $72\text{ fm}$
(D) $150\text{ fm}$
Assertion (A) : Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion.
Reason (R) : For heavy nuclei, binding energy per nucleon increases with increasing $Z$ while for light nuclei, it decreases with increasing $Z$.
(a) (i) Write any two features of nuclear forces.
(ii) If both the number of protons and the neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction ? Explain.
OR
(b) (i) Draw the number of scattered particles versus the scatte...
Assertion (A) : During formation of a nucleus, the mass defect produced is the source of the binding energy of the nucleus.
Reason (R) : For all nuclei, the value of binding energy per nucleon increases with mass number.
Isotones are the nuclides having :
(A) same mass numbers
(B) same atomic numbers
(C) same neutron number, but different atomic number
(D) different neutron number, and different mass number
Which of the following figures correctly represent the shape of curve of binding energy per nucleon as a function of mass number?
(a) Define 'Mass defect' and 'Binding energy' of a nucleus. Describe 'Fission process' on the basis of binding energy per nucleon.
(b) A deuteron contains a proton and a neutron and has a mass of $2.013553 \text{ u}$. Calculate the mass defect for it in $\text{u}$ and its energy equivalence in $\tex...
(a) Show the variation of binding energy per nucleon with mass number. Write the significance of the binding energy curve.
(b) Two nuclei with lower binding energy per nucleon form a nuclei with more binding energy per nucleon.
(i) What type of nuclear reaction is it ?
(ii) Whether the total mass of...
Assertion (A) : Nuclear fission reactions are responsible for energy generation in the Sun.
Reason (R) : Light nuclei fuse together in the nuclear fission reactions.
(a) Differentiate between nuclear fission and fusion. (b) The fission properties of ${}_{94}\text{Pu}^{239}$ are very similar to those of ${}_{92}\text{U}^{235}$. How much energy (in MeV), is released if all the atoms in 1 g of pure ${}_{94}\text{Pu}^{239}$ undergo fission ? The average energy relea...
(a) Consider the following nuclides :
$_6^{12}\text{C}$, $_{80}^{198}\text{Hg}$, $_6^{14}\text{C}$, $_{79}^{197}\text{Au}$
Group them into isotopes and isotones.
(b) How does the size of a nucleus depend on its mass number $\text{A}$ ? Hence prove that the density of nucleus is a constant, indepe...
Differentiate between nuclear fission and nuclear fusion. Give one example for each with nuclear reaction.
Assertion (A) : The binding energy per nucleon is practically constant for mass number in the range ($30 < A < 170$).
Reason (R) : Nuclear forces between the nucleons for mass numbers in the range ($30 < A < 170$) are not short-range.
Inside a nucleus, the nuclear forces between proton and proton, proton and neutron, neutron and neutron are $F_{\text{pp}}$, $F_{\text{pn}}$ and $F_{\text{nn}}$ respectively. Then :
(A) $F_{\text{pp}} > F_{\text{pn}} > F_{\text{nn}}$
(B) $F_{\text{pn}} > F_{\text{nn}} > F_{\text{pp}}$
(C) $F_{\text{...
Define binding energy (BE) of a nucleus. An unstable nucleus has mass number $\text{A} = 240$ and $\frac{\text{BE}}{\text{A}} = 7.6\text{ MeV}$. It splits in two fragments, each of $\text{A} = 120$ with $\frac{\text{BE}}{\text{A}} = 8.5\text{ MeV}$. Calculate the energy released.
Isotones are nuclides having :
(A) same number of neutrons but different number of protons
(B) same number of protons but different number of neutrons
(C) same number of protons and also same number of neutrons
(D) different number of protons and also different number of neutrons
(a) Define atomic mass unit (u).
(b) Calculate the energy required to separate a deuteron into its constituent parts (a proton and a neutron). Given :
$m(D) = 2.014102 \text{ u}$
$m_{\text{H}} = 1.007825 \text{ u}$
$m_{\text{n}} = 1.008665 \text{ u}$
Draw a graph showing variation of binding energy per nucleon as a function of mass number $A$. The binding energy per nucleon for heavy nuclei ($A > 170$) decreases with increase in mass number. Explain its significance.
(a) Consider the following nuclides :
${}^{12}_{6}\text{C}$, ${}^{198}_{80}\text{Hg}$, ${}^{14}_{6}\text{C}$, ${}^{197}_{79}\text{Au}$
Group them into isotopes and isotones.
(b) How does the size of a nucleus depend on its mass number A ? Hence prove that the density of nucleus is a constant, indepe...
Define binding energy of a nucleus. Differentiate between nucleus fusion and nuclear fission, giving one example of each.
Differentiate between nuclear fission and nuclear fusion, giving one example for each.
(a) Distinguish between isotopes and isobars, giving one example for each.
(b) Derive the relation between atomic mass unit (u) and electron volt (eV).
Nuclides with the same number of neutrons are called :
(A) Isobars
(B) Isotones
(C) Isotopes
(D) Isomers
A fast-moving neutron collides with the nucleus of Plutonium (Pu), thereby producing Xenon (Xe) and Zirconium (Zr) along with neutrons.
(I) Write the nuclear fission reaction.
(II) Find the energy released in the above nuclear reaction.
Given atomic masses:
$m(^{239}_{\ 94}\text{Pu}) = 239.052157\...
Assertion (A) : Nuclear forces are always attractive in nature.
Reason (R) : Nuclear forces are charge-dependent forces.
Suppose that an electron is revolving around the nucleus of a hydrogen atom in the orbit of radius $0\cdot48\text{ \AA}$. Find the magnitude and direction of the electrostatic force acting on the electron.
(a) Differentiate between isobars and isotones.
(b) Show that the nuclear density is independent of mass number A of a nucleus.
Calculate the mass of an $\alpha$-particle in atomic mass unit (u). Given,
Mass of a normal helium atom $= 4.002603 ext{ u}$
Mass of carbon atom $= 1.9926 imes 10^{-26} ext{ kg}$
When a neutron collides with $^{235}_{\ 92} ext{U}$, the nucleus gives $^{140}_{\ 54} ext{Xe}$ and $^{94}_{\ 38} ext{Sr}$ as fission products and two neutrons are ejected. Calculate the mass defect and the energy released (in $ ext{MeV}$) in the process. Given :
$\text{m}
\left(^{235}_{\ 92} ext{U}...
Inside a nucleus, the nuclear forces between proton and proton, proton and neutron, neutron and neutron are $F_{pp}$, $F_{pn}$ and $F_{nn}$ respectively. Then :
(A) $F_{pp} > F_{pn} > F_{nn}$
(B) $F_{pn} > F_{nn} > F_{pp}$
(C) $F_{nn} > F_{pp} > F_{pn}$
(D) $F_{pp} = F_{pn} = F_{nn}$
(a) Consider the so-called 'D-T reaction' (Deuterium-Tritium reaction). In a thermonuclear fusion reactor, the following nuclear reaction occurs :
${}_{1}^{2}\text{H} + {}_{1}^{3}\text{H} \longrightarrow {}_{2}^{4}\text{He} + {}_{0}^{1}\text{n} + \text{Q}$
Find the amount of energy released in the r...
Assertion (A) : The binding energy per nucleon is practically constant for mass number in the range ($30 < A < 170$).\nReason (R) : Nuclear forces between the nucleons for mass numbers in the range ($30 < A < 170$) are not short-range.
Differentiate between 'nuclear fission' and 'nuclear fusion'. Briefly discuss one example of each.
Calculate the binding energy per nucleon (in $\text{MeV}$) of a helium nucleus $\left(_2^4\text{He}\right)$.
Given : $m(_2^4\text{He}) = 4\cdot002603\text{ u}$
$m_{\text{n}} = 1\cdot008665\text{ u}$
$m_{\text{H}} = 1\cdot007825\text{ u}$
$1\text{ u} = 931\cdot5\text{ MeV/c}^2$
In a Rutherford scattering experiment, when an alpha particle of mass $m_1$ approaches a target nucleus of charge $Ze$ and mass $m_2$, the distance of the closest approach is $d_0$. The energy of the particle is :
(A) directly proportional to $Z$
(B) inversely proportional to $Z$
(C) directly pro...
Define binding energy (BE) of a nucleus. An unstable nucleus has mass number $A = 240$ and $\frac{\text{BE}}{\text{A}} = 7.6\text{ MeV}$. It splits in two fragments, each of $A = 120$ with $\frac{\text{BE}}{\text{A}} = 8.5\text{ MeV}$. Calculate the energy released.
What is thermonuclear fusion ?\nCalculate the energy released in $\text{MeV}$ in the fusion reaction given below :\n$_1^2\text{H} + _1^3\text{H} \longrightarrow _2^4\text{He} + \text{n}$\nGiven : $\text{m}(_1^2\text{H}) = 2.014102\text{ u}$, $\text{m}(_1^3\text{H}) = 3.016049\text{ u}$, $\text{m}(_2...
Assertion (A): Nuclei having mass number about $60$ are least stable..
Reason (R): When two or more light nuclei are combined into a heavier nucleus then the binding energy per nucleon will decrease.
Q.20. Binding energy per nucleon vs mass number curve for nuclei is shown in the figure. W, X, Y and Z are four nuclei indicated on the curve. Identify which of the following nuclei is most likely to undergo
(i) Nuclear Fission
(ii) Nuclear Fusion. Justify your answer. (for V.I. Candidates) Binding energy per nucleon and mass number of the following nuclei are given in the below table: Nuclei W (Binding energy per nucleon (MeV) 7.5, Mass number 190), X (Binding energy per nucleon (MeV) 8.0, Mass number 90), Y (Binding ener...
The carbon isotope $^{12}_{6} ext{C}$ has a nuclear mass of 12.000000 u. Calculate the binding energy of its nucleus. Given $ ext{m}_{ ext{p}} = 1.007825 ext{ u}$; $ ext{m}_{ ext{n}} = 1.008665 ext{ u}$.
(a) Define atomic mass unit (u). (b) Calculate the energy required to separate a deuteron into its constituent parts (a proton and a neutron). Given : $\text{m(D)} = 2\cdot014102 \text{ u}$, $\text{m}_\text{H} = 1\cdot007825 \text{ u}$, $\text{m}_\text{n} = 1\cdot008665 \text{ u}$
A positively charged particle of mass m, moving with velocity v is bombarded on a heavy nucleus of charge Ze. Its distance of closest approach from the nucleus is proportional to :
(A) $\frac{Z}{mv^2}$
(B) $\frac{v^2}{Zm}$
(C) $v^2$
(D) $\frac{Zv^2}{m}$
Differentiate between mass defect and binding energy per nucleon. The binding energy per nucleon is nearly constant in the range $30 < A < 170$. Why ?
(a) Explain two main features of the plot of the binding energy per nucleon versus the mass number of the nuclei. Mention two conclusions that can be drawn from these features.
OR
(b) Briefly explain the observations made in Geiger-Marsden experiment. Write the important conclusions drawn about the ...
The binding energy per nucleon of $_8\text{O}^{16}$ is $7.97\text{ MeV}$ and that of $_8\text{O}^{17}$ is $7.75\text{ MeV}$. The energy (in $\text{MeV}$) required to remove a neutron from $_8\text{O}^{17}$ is :
(a) $0.42\text{ MeV}$
(b) $7.86\text{ MeV}$
(c) $4.23\text{ MeV}$
(d) $3.64\text{ MeV}$
The binding energy per nucleon is lower : (a) for light nuclei only (b) for heavy nuclei only (c) for nuclei of middle mass numbers only (d) both for the light nuclei and the heavy nuclei
(a) Obtain the relationship between atomic mass unit (u) and electron volt (eV).
(b) The mass of a ball is $0 \cdot 5 \text{ kg}$. It is totally converted into energy. Calculate the energy output in eV.
(b) What is the ratio of the nuclear density of ${}^4_2\text{He}$ and ${}^{14}_7\text{N}$ ?