Physics · Class 12 Science
Ch 13Nuclei — Class 12 Physics, concept-first.
The previous chapter on atoms left us with a striking picture: almost all the mass and all the positive charge of an atom are crammed into a tiny central core called the nucleus. The rest of the atom — the region where electrons roam — is mostly empty space.
Key concepts
Hover a concept to preview it and jump to its most relevant Q&A.
Nuclear Density Calculation
Imagine you have a bag of marbles. If you pack them tightly, the density of the bag depends only on the marbles themselves — not on how many you put in. The nucleus behaves the same way. That's the core idea.
Most relevant Q&A
- Given the mass of iron nucleus as $55.85\ \text{u}$ and $A = 56$, find the nuclear density.Preview
- Obtain approximately the ratio of the nuclear radii of the gold isotope $^{197}_{79}\text{Au}$ and the silver isotope $^{107}_{47}\text{Ag}$…Preview
- From the relation $R = R_0 A^{1/3}$, where $R_0$ is a constant and $A$ is the mass number of a nucleus, show that the nuclear matter density…Preview
Chapter contents
The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.
Introduction
The previous chapter on atoms left us with a striking picture: almost all the mass and all the positive charge of an atom are crammed into a tiny central core called the nucleus.
Atomic Masses and Composition of Nucleus
The mass of a single atom is extraordinarily small when measured in kilograms. A carbon-12 atom, for instance, has a mass of only kg.
Size of the Nucleus
The story of the nucleus begins with Rutherford. After his famous gold-foil experiment, he knew that the atom’s positive charge and nearly all its mass were concentrated in a tiny central region — the…
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Mass-energy and Nuclear Binding Energy
The story of nuclear binding energy begins with a profound idea from Einstein’s special relativity: mass and energy are not separate quantities.
Mass – Energy
Before Einstein’s theory of special relativity, physicists treated mass and energy as two completely separate quantities.
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Nuclear Binding Energy
You might think that the mass of a nucleus is simply the sum of the masses of its individual protons and neutrons. After all, a nucleus is made of these particles.
Nuclear Force
The electrons in an atom are held by the familiar Coulomb force between opposite charges. But the nucleus is a different world.
Radioactivity
Radioactivity was discovered in 1896 by Henri Becquerel, quite by accident. While studying how certain compounds glow after being exposed to visible light, Becquerel placed some uranium-potassium sulp…
Nuclear Energy
The curve of binding energy per nucleon () against mass number (Figure 13.1 in the textbook) reveals a crucial fact: for nuclei with mass numbers between and , the binding energy per nucleon is nearly…
Fission
When we move beyond the natural radioactive decays that happen spontaneously, a whole new world opens up: nuclear reactions.
Nuclear Fusion – Energy Generation in Stars
When two light nuclei merge to form a heavier nucleus, the process is called nuclear fusion. Because the heavier nucleus is more tightly bound (as seen from the binding energy per nucleon curve), the…
Controlled Thermonuclear Fusion
The energy that powers stars, including our Sun, comes from nuclear fusion — the process in which very light nuclei combine to form a heavier nucleus.
Summary
- Nuclear composition: A nucleus is made of protons and neutrons (nucleons). Atomic number = number of protons; mass number = total nucleons.
Points to Ponder
1. The density of nuclear matter is roughly constant across all nuclei — it does not depend on the mass number .
Exercises
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- 13.3(a) Two stable isotopes of lithium $^{6}_{3}\text{Li}$ and $^{7}_{3}\text{Li}$ have respective abundances of 7.5% and 92.5%. These isotopes…Free
- 13.4The three stable isotopes of neon: $^{20}_{10}\text{Ne}$, $^{21}_{10}\text{Ne}$ and $^{22}_{10}\text{Ne}$ have respective abundances of 90.5…Free
- 13.5Obtain the binding energy (in MeV) of a nitrogen nucleus $^{14}_{7}\text{N}$, given $m\left(^{14}_{7}\text{N}\right) = 14.00307\ \text{u}$.Free
- 13.11Obtain the binding energy of the nuclei $^{56}_{26}\text{Fe}$ and $^{209}_{83}\text{Bi}$ in units of MeV from the following data: $m\left(^{…Preview
- 13.11Obtain approximately the ratio of the nuclear radii of the gold isotope $^{197}_{79}\text{Au}$ and the silver isotope $^{107}_{47}\text{Ag}$…Preview
- 13.12Find the Q-value and the kinetic energy of the emitted $\alpha$-particle in the $\alpha$-decay of (a) $^{226}_{88}\text{Ra}$ and (b) $^{220}…Preview
- 13.13The radionuclide $^{11}\text{C}$ decays according to $$^{11}_{6}\text{C} \rightarrow {}^{11}_{5}\text{B} + e^{+} + \nu \ : \ T_{1/2} = 20.3\…Preview
- 13.14The nucleus $^{23}_{10}\text{Ne}$ decays by $\beta^{-}$ emission. Write down the $\beta$-decay equation and determine the maximum kinetic en…Preview
- 13.15A given coin has a mass of $3.0\ \text{g}$. Calculate the nuclear energy that would be required to separate all the neutrons and protons fro…Preview
- 13.15The Q value of a nuclear reaction $A + b \rightarrow C + d$ is defined by $Q = [\,m_A + m_b - m_C - m_d\,]c^2$ where the masses refer to the…Preview
- 13.16Suppose, we think of fission of a $^{56}_{26}\text{Fe}$ nucleus into two equal fragments, $^{28}_{13}\text{Al}$. Is the fission energeticall…Preview
- 13.16Write nuclear reaction equations for (i) $\alpha$-decay of $^{226}_{88}\text{Ra}$ (ii) $\alpha$-decay of $^{242}_{94}\text{Pu}$ (iii) $\beta…Preview
- 13.17The fission properties of $^{239}_{94}\text{Pu}$ are very similar to those of $^{235}_{92}\text{U}$. The average energy released per fission…Preview
- 13.17A 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?Preview
- 13.18A 1000 MW fission reactor consumes half of its fuel in 5.00 y. How much $^{235}_{92}\text{U}$ did it contain initially? Assume that the reac…Preview
- 13.19How long can an electric lamp of $100\ \text{W}$ be kept glowing by fusion of $2.0\ \text{kg}$ of deuterium? Take the fusion reaction as $^{…Preview
- 13.19The normal activity of living carbon-containing matter is found to be about 15 decays per minute for every gram of carbon. This activity ari…Preview
- 13.20Calculate the height of the potential barrier for a head on collision of two deuterons. (Hint: The height of the potential barrier is given…Preview
- 13.20Obtain the amount of $^{60}_{27}\text{Co}$ necessary to provide a radioactive source of 8.0 mCi strength. The half-life of $^{60}_{27}\text{…Preview
- 13.21From the relation $R = R_0 A^{1/3}$, where $R_0$ is a constant and $A$ is the mass number of a nucleus, show that the nuclear matter density…Preview
- 13.21The half-life of $^{90}_{38}\text{Sr}$ is 28 years. What is the disintegration rate of 15 mg of this isotope?Preview
- 13.22For the $\beta^{+}$ (positron) emission from a nucleus, there is another competing process known as electron capture (electron from an inner…Preview
Additional Exercises
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- 13.23In a periodic table the average atomic mass of magnesium is given as 24.312 u. The average value is based on their relative natural abundanc…Free
- 13.24The neutron separation energy is defined as the energy required to remove a neutron from the nucleus. Obtain the neutron separation energies…Free
- 13.25A source contains two phosphorous radio nuclides $^{32}_{15}\text{P}$ ($T_{1/2}$ = 14.3d) and $^{33}_{15}\text{P}$ ($T_{1/2}$ = 25.3d). Init…Free
- 13.26Under certain circumstances, a nucleus can decay by emitting a particle more massive than an $\alpha$-particle. Consider the following decay…Preview
- 13.27Consider the fission of $^{238}_{92}\text{U}$ by fast neutrons. In one fission event, no neutrons are emitted and the final end products, af…Preview
- 13.28Consider the D-T reaction (deuterium-tritium fusion) $$^{2}_{1}\text{H} + {}^{3}_{1}\text{H} \rightarrow {}^{4}_{2}\text{He} + n$$ (a) Calcu…Preview
- 13.30Calculate and compare the energy released by a) fusion of 1.0 kg of hydrogen deep within Sun and b) the fission of 1.0 kg of $^{235}\text{U}…Preview
- 13.31Suppose 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…Preview
Exemplar Problems
Higher-order thinking / exemplar-style practice problems.
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- Q1The gravitational force between a H-atom and another particle of mass $m$ will be given by Newton's law: $F = G\dfrac{M\,m}{r^2}$, where $r$…Free
- Q2Heavy stable nuclei have more neutrons than protons. This is because of the fact that (a) neutrons are heavier than protons. (b) electrostat…Free
- Q3In a nuclear reactor, moderators slow down the neutrons which come out in a fission process. The moderator used have light nuclei. Heavy nuc…Free
- Q4Fusion processes, like combining two deuterons to form a He nucleus are impossible at ordinary temperatures and pressure. The reasons for th…Preview
- Q5$^{3}_{2}\text{He}$ and $^{3}_{1}\text{H}$ nuclei have the same mass number. Do they have the same binding energy?Preview
- Q6Which one of the following cannot emit radiation and why? Excited nucleus, excited electron.Preview
- Q7In pair annihilation, an electron and a positron destroy each other to produce gamma radiation. How is the momentum conserved?Preview
- Q8Why do stable nuclei never have more protons than neutrons?Preview
- Q9Are the nucleons fundamental particles, or do they consist of still smaller parts? One way to find out is to probe a nucleon just as Rutherf…Preview
- Q10A nuclide 1 is said to be the mirror isobar of nuclide 2 if $Z_1 = N_2$ and $Z_2 = N_1$. (a) What nuclide is a mirror isobar of $^{23}_{11}\…Preview
- Q11Deuteron is a bound state of a neutron and a proton with a binding energy $B = 2.2\ \text{MeV}$. A $\gamma$-ray of energy $E$ is aimed at a…Preview
- Q12The 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…Preview
- Q13Nuclei with magic no. of proton $Z = 2, 8, 20, 28, 50, 82$ and magic no. of neutrons $N = 2, 8, 20, 28, 50, 82$ and $126$ are found to be ve…Preview
Sample & Board Papers
Sample papers and previous-year board questions for this subject.
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- Q1Explain the terms mass defect and binding energy. How are they related ?Preview
- Q2(a) Distinguish between isotopes and isobars, giving one example for each. (b) Why is the mass of a nucleus always less than the sum of the…Preview
- Q3(a) Draw a plot showing the variation of potential energy of a pair of nucleons as a function of their separation. Mark the regions where th…Preview