Here are 20 Important Questions & Answers from CBSE Class 12 Physics
Chapter 13: Nuclei
(2026–27 syllabus). These are written in exam-oriented format.
Q1. Define nuclear radius and write its expression.
Ans:
The nuclear radius is the effective distance from the center of the nucleus up to which nuclear force is significant. It represents the size of the nucleus. Experimentally, it is found that nuclear radius is not constant but depends on the mass number (A) of the nucleus. The relation is given by
( R = R_0 A^{1/3} ), where ( R_0 \approx 1.2 \times 10^{-15} , m ).
This shows that nuclear radius increases slowly with mass number. It implies that nuclear density remains nearly constant for all nuclei. This is because volume is proportional to A, and mass is also proportional to A.
Q2. What is nuclear density? Why is it constant?
Ans:
Nuclear density is defined as the mass per unit volume of a nucleus. It is given by
( \rho = \frac{m}{V} ).
Since nuclear mass is proportional to mass number (A) and nuclear volume is proportional to ( A^{1/3} )^3 = A, the density becomes independent of A. Hence, nuclear density is nearly constant for all nuclei and is approximately ( 2.3 \times 10^{17} , kg/m^3 ). This extremely high value shows that nuclei are very tightly packed. It also indicates that nuclear matter is incompressible in nature.
Q3. Define mass defect.
Ans:
Mass defect is defined as the difference between the total mass of separate nucleons (protons and neutrons) and the actual mass of the nucleus. It is written as
( \Delta m = Zm_p + (A-Z)m_n – M ).
This missing mass is converted into binding energy according to Einstein’s equation ( E = \Delta m c^2 ). Mass defect indicates the stability of the nucleus. Larger mass defect means higher binding energy and more stable nucleus. It is an important concept in nuclear physics to explain nuclear reactions and energy release.
Q4. What is binding energy of a nucleus?
Ans:
Binding energy is the energy required to completely separate a nucleus into its constituent protons and neutrons. It is also the energy released when a nucleus is formed from free nucleons. It is given by
( BE = \Delta m c^2 ).
Binding energy represents nuclear stability. Higher binding energy means more stable nucleus. Binding energy per nucleon is a better measure of stability. Iron (Fe) has the highest binding energy per nucleon, making it the most stable nucleus. This concept explains both nuclear fission and fusion processes.
Q5. Explain binding energy per nucleon.
Ans:
Binding energy per nucleon is defined as the average energy required to remove one nucleon from the nucleus. It is given by
( BE/A ).
It is a measure of nuclear stability. A higher value of BE/A means the nucleus is more stable. For light nuclei, BE/A increases with mass number, while for heavy nuclei it decreases slightly. The maximum value occurs near iron (A ≈ 56). This variation explains why energy is released in both nuclear fission and fusion processes.
Q6. What is nuclear force? Write its properties.
Ans:
Nuclear force is the strong attractive force between nucleons (protons and neutrons) that holds the nucleus together. It is the strongest force in nature but acts only at very small distances (~1–3 fm). Its properties include:
- It is charge independent (same between p-p, n-n, p-n).
- It is short-range force.
- It shows saturation property (each nucleon interacts with nearby nucleons only).
- It is attractive at normal distances but repulsive at very small distances.
These properties explain nuclear stability.
Q7. What is radioactivity?
Ans:
Radioactivity is the spontaneous disintegration of unstable nuclei with emission of α, β, and γ radiations. It is a random and spontaneous process not affected by temperature, pressure, or chemical state. Radioactive decay occurs due to instability of nuclei having excess neutrons or protons. The decay follows exponential law
( N = N_0 e^{-\lambda t} ).
It is widely used in medical treatment, radiocarbon dating, and nuclear energy production. Radioactive elements include uranium, radium, etc.
Q8. Define half-life of a radioactive substance.
Ans:
Half-life is the time required for half of the radioactive nuclei in a sample to decay. It is denoted by ( T_{1/2} ). It is related to decay constant by
( T_{1/2} = \frac{0.693}{\lambda} ).
Half-life is independent of the initial quantity of the substance. It is a characteristic property of each radioactive isotope. Different isotopes have different half-lives ranging from fractions of a second to millions of years.
Q9. What is mean life of a radioactive substance?
Ans:
Mean life is the average lifetime of all radioactive nuclei in a sample before decay. It is denoted by ( \tau ) and is related to decay constant by
( \tau = \frac{1}{\lambda} ).
Mean life is slightly greater than half-life. It represents statistical average of decay times of all nuclei. It helps in understanding long-term decay behavior of radioactive substances.
Q10. Differentiate between nuclear fission and fusion.
Ans:
Nuclear fission is the splitting of a heavy nucleus into lighter nuclei with release of energy, e.g., uranium-235. Nuclear fusion is the combination of two light nuclei to form a heavier nucleus with release of energy, e.g., hydrogen fusion in the Sun.
Fission occurs at room temperature conditions (controlled in reactors), while fusion requires extremely high temperature (~10⁷ K). Fusion releases more energy per unit mass than fission. Both processes convert mass into energy using ( E = mc^2 ).
Q11. What is Q-value of a nuclear reaction?
Ans:
Q-value is the net energy released or absorbed in a nuclear reaction. It is given by
( Q = (m_{initial} – m_{final})c^2 ).
If Q is positive, energy is released; if negative, energy is absorbed. It depends on mass difference between reactants and products. Q-value is important in determining whether a nuclear reaction is exothermic or endothermic.
Q12. Explain radioactive decay law.
Ans:
Radioactive decay law states that the rate of decay of nuclei is directly proportional to the number of undecayed nuclei present. It is expressed as
( \frac{dN}{dt} = -\lambda N ).
On solving, we get
( N = N_0 e^{-\lambda t} ).
This shows exponential decay behavior. The decay constant ( \lambda ) is probability of decay per unit time. This law is fundamental in nuclear physics.
Q13. What is activity of a radioactive substance?
Ans:
Activity is the rate of decay of radioactive nuclei. It is given by
( A = \lambda N ).
Its SI unit is becquerel (Bq), where 1 Bq = 1 disintegration per second. Activity decreases with time as the number of nuclei decreases. It follows exponential decay law similar to number of nuclei.
Q14. Why is heavy water used as a moderator?
Ans:
Heavy water (D₂O) is used as a moderator in nuclear reactors because it slows down fast neutrons without absorbing them significantly. Ordinary water absorbs neutrons more, reducing efficiency. Heavy water contains deuterium, which has very low neutron absorption cross-section. Thus, it effectively reduces neutron speed and helps sustain chain reaction in reactors.
Q15. What is nuclear reactor?
Ans:
A nuclear reactor is a device used to control nuclear fission chain reactions. It produces controlled energy using uranium or plutonium fuel. Main components include fuel rods, moderator, control rods, coolant, and shielding. Control rods (cadmium/boron) absorb excess neutrons to control reaction rate. Reactors are used for electricity generation and research.
Q16. What is binding energy curve?
Ans:
The binding energy per nucleon vs mass number graph shows variation of nuclear stability. It rises sharply for light nuclei, peaks around A ≈ 56 (iron), and then slowly decreases for heavy nuclei. This curve explains why energy is released in fusion (light nuclei combine) and fission (heavy nuclei split).
Q17. What is isotopes, isobars, and isotones?
Ans:
Isotopes are atoms with same atomic number but different mass numbers. Isobars have same mass number but different atomic numbers. Isotones have same number of neutrons but different protons. These classifications help in understanding nuclear structure.
Q18. Why is nucleus stable?
Ans:
Nuclear stability is due to strong nuclear force acting between nucleons. Stability depends on neutron-proton ratio and binding energy per nucleon. Stable nuclei have optimal n/p ratio and high binding energy. Too many or too few neutrons lead to instability and radioactive decay.
Q19. What is alpha decay?
Ans:
Alpha decay is a type of radioactive decay in which a nucleus emits an alpha particle (helium nucleus). Atomic number decreases by 2 and mass number decreases by 4. It commonly occurs in heavy nuclei like uranium and radium. It reduces nuclear instability.
Q20. What is beta decay?
Ans:
Beta decay is a process in which a neutron converts into a proton (β⁻ decay) or proton converts into neutron (β⁺ decay). It changes atomic number but mass number remains constant. It helps unstable nuclei achieve stability by adjusting neutron-proton ratio.