The atomic nucleus is the dense central part of an atom where nearly all its mass and positive charge are concentrated. It was discovered by Ernest Rutherford in 1911 through his famous alpha scattering experiment. This discovery changed our understanding of atomic structure completely.
An atom has a nucleus at the centre, made of protons (positively charged particles) and neutrons (neutral particles), collectively called nucleons. Electrons revolve around the nucleus at comparatively larger distances.
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Atomic Number (Z): Number of protons in the nucleus.
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Mass Number (A): Total number of protons and neutrons.
An atom is represented as:
ZAX_{Z}^{A}X
Here, X is the chemical symbol of the element.
Class 12 Physics Nuclei Notes | Detailed Explanation, Questions & Answers
Properties of the Nucleus
Mass and Size
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Mass of a nucleus ≈ A × mass of nucleon – mass defect.
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Mass of proton ≈ 1.007276 u, neutron ≈ 1.008665 u.
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Radius formula:
R=R0A1/3R = R_0 A^{1/3}
Where R0=1.2×10−15 mR_0 = 1.2 \times 10^{-15} \, m.
Example: For A = 64, R=1.2×641/3=4.8 fmR = 1.2 × 64^{1/3} = 4.8 \, fm.
Nuclear Charge
All the positive charge in an atom comes from protons in the nucleus. Electrons revolve outside, making the atom electrically neutral.
Mass Defect and Binding Energy
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Mass Defect (Δm): Difference between the total mass of nucleons separately and the actual mass of the nucleus.
Δm=Zmp+(A−Z)mn−mnucleusΔm = Zm_p + (A – Z)m_n – m_{nucleus}
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Binding Energy (BE): Energy required to break the nucleus into individual protons and neutrons.
BE=Δm×c2BE = Δm × c^2
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Binding Energy per Nucleon: BEA\frac{BE}{A} shows average stability per nucleon.
The binding energy curve peaks around Iron (Fe) at A ≈ 56, showing iron nuclei are most stable.
Nuclear Density
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Density of nucleus is nearly constant for all nuclei.
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Formula:
ρ=massvolume=Amn43πR3ρ = \frac{mass}{volume} = \frac{A m_n}{\frac{4}{3}\pi R^3}
Since R∝A1/3R \propto A^{1/3}, density becomes independent of A.
Value: ρ≈2.3×1017 kg/m3ρ ≈ 2.3 × 10^{17} \, kg/m^3.
Nuclear Forces and Stability
Nuclear Force
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Strongest known force in nature.
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Attractive, charge-independent, short-range (~1–2 fm).
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Becomes repulsive at very small distances (< 0.5 fm) to prevent collapse of nucleus.
Stability and Neutron–Proton Ratio
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Light nuclei: N/Z ≈ 1 is stable.
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Heavy nuclei: Require more neutrons than protons for stability.
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Magic Numbers: 2, 8, 20, 28, 50, 82, 126 → Highly stable nuclei with completely filled shells.
Radioactivity
Law of Radioactive Decay
If NN nuclei are present at time tt:
N=N0e−λtN = N_0 e^{-λt}
Where:
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N0N_0: Initial nuclei
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λλ: Decay constant
Half-life: Time in which half the nuclei decay.
T1/2=0.693λT_{1/2} = \frac{0.693}{λ}
Types of Radioactive Decay
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Alpha (α) Decay:
Heavy nucleus emits a helium nucleus (α = 24He_2^4 He).
Reduces A by 4, Z by 2.Example: 92238U→90234Th+α_{92}^{238}U → _{90}^{234}Th + α
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Beta (β) Decay:
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β⁻ decay: Neutron → Proton + Electron + Antineutrino.
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β⁺ decay: Proton → Neutron + Positron + Neutrino.
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Gamma (γ) Decay:
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Emission of high-energy photons without change in A or Z.
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Nuclear Reactions
A nuclear reaction involves changes in the nucleus due to external particles or nuclei.
Conservation Laws
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Conservation of Mass Number (A)
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Conservation of Atomic Number (Z)
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Conservation of Energy and Momentum
Nuclear Fission
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A heavy nucleus splits into two lighter nuclei + neutrons + energy.
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Example:
92235U+n→56141Ba+3692Kr+3n+Energy_{92}^{235}U + n → _{56}^{141}Ba + _{36}^{92}Kr + 3n + Energy
Used in nuclear reactors for electricity generation.
Nuclear Fusion
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Two light nuclei combine to form a heavier nucleus + energy.
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Example: In Sun:
411H→24He+2e++2νe+Energy4_1^1H → _2^4He + 2e^+ + 2ν_e + Energy
Fusion releases enormous energy, much greater than fission.
Nuclear Models
Liquid Drop Model
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Treats nucleus like a drop of liquid.
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Explains binding energy formula and nuclear fission.
Shell Model
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Nucleons move in discrete energy levels like electrons in atoms.
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Explains magic numbers and nuclear spins.
Applications of Nuclei
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Nuclear Power Plants: Controlled fission.
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Medical Field: Radiotherapy, cancer treatment, PET scans.
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Industrial Use: Thickness measurement, sterilization.
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Agriculture: Radiation-induced mutation for better crops.
Important Formulas
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Nuclear Radius: R=R0A1/3R = R_0 A^{1/3}
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Mass Defect: Δm=Zmp+(A−Z)mn−mnucleusΔm = Zm_p + (A – Z)m_n – m_{nucleus}
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Binding Energy: BE=Δm×c2BE = Δm × c^2
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Half-life: T1/2=0.693λT_{1/2} = \frac{0.693}{λ}
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Activity: A=λNA = λN
Sample Problems
Problem 1: Radius of A=27A = 27 nucleus?
Solution: R=1.2×271/3=3.6 fmR = 1.2 × 27^{1/3} = 3.6 \, fm.
Problem 2: Half-life of 10 h. Initial nuclei = 1600. Nuclei after 30 h?
Solution: 30 h = 3 half-lives → Remaining = 1600 × (1/2)³ = 200 nuclei.
Quick Revision Points
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Nucleons = Protons + Neutrons
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Mass Defect → Binding Energy → Stability
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α: A–4, Z–2; β⁻: Z+1; β⁺: Z–1; γ: only energy loss
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Fusion = Sun’s energy; Fission = Reactors & bombs
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Magic Numbers = Extra stability
Objective Question –Semiconductor Electronics Notes
Q1. The radius of a nucleus is proportional to which of the following?
a) A
b) A¹ᐟ³
c) A²
d) A³
Answer:
The radius RR of a nucleus is given by R=R0A1/3R = R_0 A^{1/3}. Hence it is proportional to A¹ᐟ³. Correct option: b
Q2. Which particle is emitted during alpha decay?
a) Electron
b) Proton
c) Helium nucleus
d) Positron
Answer:
Alpha decay emits a Helium nucleus containing 2 protons and 2 neutrons. Correct option: c
Q3. The binding energy per nucleon is maximum for:
a) Uranium
b) Iron
c) Hydrogen
d) Thorium
Answer:
The binding energy per nucleon is maximum for Iron (Fe) at mass number A ≈ 56, making it the most stable nucleus. Correct option: b
Q4. The unit of radioactive decay constant (λ) is:
a) Second
b) Second⁻¹
c) Minute
d) No unit
Answer:
Decay constant λ has the dimension of inverse time. Hence its unit is Second⁻¹. Correct option: b
Q5. In beta minus (β⁻) decay, a neutron converts into:
a) Proton + Electron + Antineutrino
b) Proton + Electron + Neutrino
c) Proton only
d) Electron only
Answer:
In β⁻ decay: n→p+e−+νˉen → p + e⁻ + \barν_e. Hence correct option: a
Q6. Which law governs radioactive decay?
a) Newton’s law
b) Ohm’s law
c) Exponential law
d) Coulomb’s law
Answer:
Radioactive decay follows the exponential law: N=N0e−λtN = N_0 e^{-λt}. Correct option: c
Q7. Half-life formula is:
a) T1/2=0.693λT_{1/2} = \frac{0.693}{λ}
b) T1/2=λ0.693T_{1/2} = \frac{λ}{0.693}
c) T1/2=λ×0.693T_{1/2} = λ × 0.693
d) T1/2=1λT_{1/2} = \frac{1}{λ}
Answer:
The half-life is given by T1/2=0.693λT_{1/2} = \frac{0.693}{λ}. Correct option: a
Q8. The density of the nucleus is:
a) Different for different nuclei
b) Same for all nuclei
c) Zero
d) Infinite
Answer:
Nuclear density is constant for all nuclei, about 2.3×1017kg/m32.3 × 10^{17} kg/m^3. Correct option: b
Q9. Which of the following has the highest penetrating power?
a) Alpha rays
b) Beta rays
c) Gamma rays
d) Neutrons
Answer:
Gamma rays have highest penetrating power among all radiations. Correct option: c
Q10. Mass defect is related to:
a) Atomic number only
b) Binding energy
c) Radius of nucleus
d) Half-life
Answer:
Mass defect represents the mass converted into binding energy using E=Δmc2E = Δm c². Correct option: b
Q11. The process in which a heavy nucleus splits into two lighter nuclei is called:
a) Fusion
b) Fission
c) Radioactivity
d) Ionization
Answer:
The splitting of heavy nuclei into lighter ones is called fission. Correct option: b
Q12. The process taking place in the Sun to produce energy is:
a) Nuclear fission
b) Nuclear fusion
c) Radioactive decay
d) Pair production
Answer:
The Sun produces energy through nuclear fusion of hydrogen into helium. Correct option: b
Q13. Magic numbers are related to:
a) Atomic mass
b) Atomic number
c) Stability of nuclei
d) Decay constant
Answer:
Magic numbers like 2, 8, 20, 28, 50, 82, 126 correspond to extra stability of nuclei. Correct option: c
Q14. Unit of radioactive activity is:
a) Joule
b) Becquerel
c) Newton
d) Tesla
Answer:
Activity is measured in Becquerel (Bq) = 1 decay/sec. Correct option: b
Q15. Alpha particles have:
a) High ionization, low penetration
b) Low ionization, high penetration
c) High ionization, high penetration
d) Low ionization, low penetration
Answer:
Alpha particles have high ionization power but low penetration power. Correct option: a
Q16. The daughter nucleus after alpha decay has:
a) A – 2, Z – 4
b) A – 4, Z – 2
c) A – 4, Z – 4
d) A – 2, Z – 2
Answer:
In α decay, A decreases by 4 and Z decreases by 2. Correct option: b
Q17. The equation N=N0e−λtN = N_0 e^{-λt} represents:
a) Growth law
b) Decay law
c) Coulomb’s law
d) Hooke’s law
Answer:
This equation represents the radioactive decay law. Correct option: b
Q18. Nuclear force is:
a) Short-range, strong
b) Long-range, weak
c) Gravitational
d) Electromagnetic
Answer:
Nuclear force is strong but short-range (~1-2 fm). Correct option: a
Q19. One atomic mass unit (u) is equal to:
a) 1 kg
b) 1.66×10−27kg1.66 × 10^{-27} kg
c) 9.1×10−31kg9.1 × 10^{-31} kg
d) 3×108m/s3 × 10^8 m/s
Answer:
1 u = 1.66×10−27kg1.66 × 10^{-27} kg. Correct option: b
Q20. The energy released in nuclear reactions comes from:
a) Chemical energy
b) Heat energy
c) Mass defect
d) Electric energy
Answer:
Energy in nuclear reactions arises from mass
Short-Answer Questions-Semiconductor Electronics Notes
Q1. Define mass defect.
Answer:
Mass defect is the difference between the sum of the masses of protons and neutrons and the actual mass of the nucleus. It arises because some mass converts into binding energy according to E=Δmc2E = Δm c².
Q2. What is binding energy?
Answer:
Binding energy is the energy required to break a nucleus into its constituent protons and neutrons. It is also the energy released when a nucleus is formed from nucleons.
Q3. Define the half-life of a radioactive element.
Answer:
Half-life is the time required for half of the radioactive nuclei in a sample to decay. It is given by T1/2=0.693/λT_{1/2} = 0.693 / λ.
Q4. State the law of radioactive decay.
Answer:
The law states that the rate of decay of radioactive nuclei at any instant is proportional to the number of undecayed nuclei present at that instant: dNdt=−λN\frac{dN}{dt} = -λN.
Q5. What is the difference between nuclear fission and nuclear fusion?
Answer:
In fission, a heavy nucleus splits into two smaller nuclei with energy release, while in fusion, two light nuclei combine to form a heavier nucleus with even more energy release.
Q6. Why is nuclear density independent of mass number?
Answer:
Nuclear density depends on the number of nucleons per unit volume. Since nuclear radius R∝A1/3R \propto A^{1/3}, density becomes constant for all nuclei.
Q7. Write two uses of radioactive isotopes.
Answer:
Radioactive isotopes are used in:
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Medical diagnosis and treatment (e.g., cancer therapy).
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Tracing leaks in pipelines and studying chemical reactions.
Q8. What is the physical meaning of decay constant?
Answer:
Decay constant λλ is the probability of decay of one nucleus per unit time. A larger λλ means faster decay.
Q9. Define atomic mass unit (u).
Answer:
One atomic mass unit is defined as one-twelfth of the mass of a carbon-12 atom. Numerically, 1u=1.66×10−27kg1u = 1.66 × 10^{-27} kg.
Q10. What are magic numbers in nuclear physics?
Answer:
Magic numbers are specific numbers of nucleons (2, 8, 20, 28, 50, 82, 126) for which nuclei are especially stable.
Long-Answer Questions-Semiconductor Electronics Notes
Q1. Derive the law of radioactive decay.
Answer:
Let NN be the number of undecayed nuclei at time tt. The rate of decay is proportional to NN:
dNdt=−λN\frac{dN}{dt} = -λN
Separating variables and integrating, we get:
lnN=−λt+C\ln N = -λt + C
At t=0,N=N0t = 0, N = N_0, so C=lnN0C = \ln N_0.
Hence,
N=N0e−λtN = N_0 e^{-λt}
This is the exponential law of decay.
Q2. Explain nuclear binding energy and plot binding energy per nucleon vs mass number curve.
Answer:
Binding energy per nucleon is given by:
B.E./A=Δmc2AB.E./A = \frac{Δm c^2}{A}
The curve shows:
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For low mass nuclei (A < 56), B.E./A increases with A.
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Maximum at A = 56 (Iron).
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For A > 56, B.E./A decreases with A.
This explains why fission occurs in heavy nuclei and fusion in light nuclei.
Q3. Explain nuclear fission with a reaction example.
Answer:
In fission, a heavy nucleus like 235U^{235}U absorbs a neutron and splits into two smaller nuclei, releasing energy and more neutrons:
235U+n→141Ba+92Kr+3n+Energy^{235}U + n → ^{141}Ba + ^{92}Kr + 3n + Energy
This chain reaction is the principle behind nuclear reactors and atom bombs.
Q4. Explain nuclear fusion and its importance in stars.
Answer:
Fusion is the process where light nuclei (e.g., hydrogen) combine under high temperature and pressure to form a heavier nucleus (e.g., helium), releasing enormous energy:
1H+1H→2H+e++ν+Energy^1H + ^1H → ^2H + e^+ + ν + Energy
This process powers the Sun and other stars, providing heat and light to Earth.
Q5. Discuss the properties of nuclear forces.
Answer:
Nuclear forces are:
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Strongest in nature: Much stronger than electromagnetic forces.
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Short-range: Effective only up to a few femtometers.
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Charge independent: Same between proton-proton, neutron-neutron, and proton-neutron pairs.
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Saturating: Each nucleon interacts only with nearest neighbors.
Conclusion
The study of nuclei explains the stability of matter, source of nuclear energy, and applications in power generation, medicine, and research. Concepts like mass defect, binding energy, radioactivity, fission, and fusion form the backbone of nuclear physics. Mastering these topics helps students score well in exams and understand real-world nuclear phenomena.