Definitions [21]
Define binding energy per nucleon.
Binding energy per nucleon is the least amount of energy required to liberate all of the nucleons from the nucleus.
As a result, the binding energy per nucleon is
`E_B/A`
Define unified atomic mass unit.
`1/12`th of the mass of an atom of 6C12 isotope.
With reference to Nuclear Physics, answer the following question.
Define lu (where u stands for unified atomic mass unit).
1 AMU is the average of proton rest mass and the neutron rest mass. Thus can be expressed as
1 AMU = 1.67377 × 10-27 kg
= 1.67377 × 10-24 gram
and C-12 is considered a reference for all atomic mass calculations.
Nuclear force is the strong attractive force of a totally different kind which binds protons and neutrons in the nucleus and overcomes the Coulomb repulsion between protons.
Nuclear fusion is the process in which two or more light nuclei combine to form a heavier nucleus, accompanied by the release of a large amount of energy.
Radioactivity is the phenomenon in which nuclei of a given species transform by giving out α, β, or γ rays.
α-rays are helium nuclei; β-rays are electrons. γ-rays are electromagnetic radiation of wavelengths shorter than X-rays.
The process by which an unstable nucleus transforms into another nucleus by emitting radiation is called radioactive decay.
Nuclear fission is the process in which a heavy nucleus splits into two or more lighter nuclei of nearly equal mass, accompanied by the release of a large amount of energy and neutrons.
The difference between the sum of masses of individual nucleons and the actual mass of the nucleus.
\[\Delta M=[Zm_p+(A-Z)m_n]-M\]
The average energy required to remove one nucleon from the nucleus.
\[E_{bn}=\frac{E_b}{A}\]
Controlled thermonuclear fusion is the process in which steady power is generated by heating nuclear fuel to very high temperatures so that fusion reactions occur in a controlled manner.
Atomic mass unit (u), defined as `1/12`th of the mass of the carbon (12C) atom. According to this definition,
\[1\mathrm{u}=\frac{\text{mass of one }^{12}\mathrm{C~atom}}{12}\]
\[=\frac{1.992647\times10^{-26}\mathrm{kg}}{12}\]
\[=1.660539\times10^{-27}\mathrm{kg}\]
Atomic number (Z) is defined as the number of protons present in the nucleus of an atom.
Neutron number (N) is defined as the number of neutrons present in the nucleus of an atom.
N = number of neutrons
Mass number (A) is defined as the total number of nucleons (protons and neutrons) present in the nucleus of an atom.
A = Z + N
Isotopes are atoms of the same element having the same atomic number (Z) but different mass numbers (A) or different neutron numbers (N).
Isobars are atoms of different elements having the same mass number (A) but different atomic numbers (Z).
Isotones are atoms of different elements having the same neutron number (N) but different atomic numbers (Z).
The nuclear radius is the distance from the centre of the nucleus to its surface.
The energy required to separate a nucleus completely into its individual nucleons.
\[E_b=\Delta Mc^2\]
Define one Becquerel.
One Becquerel (Bq) is defined as the activity of a quantity of radioactive samples in which one nucleus decays per second. It is the SI unit of the activity.
Formulae [3]
\[R=R_0A^{1/3}\]
Where:
R0 = 1.2 × 10−15 m = 1.2
\[E=mc^2\]
Where:
-
E = energy
-
m = mass
-
c = 3 × 108 m/s
The Q-value of a nuclear process is
Q = final kinetic energy – initial kinetic energy.
Due to conservation of mass-energy, this is also,
Q = (sum of initial masses – sum of final masses)c2
Key Points
| Property | Key Point |
|---|---|
| Very Strong | Stronger than Coulomb & gravitational forces |
| Short Range | Effective only up to a few femtometres (fm) |
| Saturation | Acts only on nearby nucleons |
| Charge Independent | Same for p–p, n–n, p–n |
| Nature | Attractive (>0.8 fm), repulsive (<0.8 fm) |
Important Questions [61]
- Show that the Density of Nucleus Over a Wide Range of Nuclei is Constant-independent of Mass Number A.
- Two nuclei may have the same radius, even though they contain different numbers of protons and neutrons. Explain.
- Calculate the Released Energy.
- James Chadwick, in 1932 studied the emission of neutral radiations when Beryllium nuclei were bombarded with alpha particles. He concluded that emitted radiations were neutrons and not photons.
- In the Study of Geiger-marsdon Experiment on Scattering of α Particles by a Thin Foil of Gold, Draw the Trajectory of α-particles in the Coulomb Field of Target Nucleus. Explain Briefly How One Gets the Information on the Size of the Nucleus from this Study.
- Two nuclei have different mass numbers A1 and A2. Are these nuclei necessarily the isotopes of the same element? Explain.
- Distinguish between isotopes and isobars.
- Two Nuclei Have Mass Numbers in the Ratio 1: 2. What is the Ratio of Their Nuclear Densities?
- The ratio of the nuclear densities of two nuclei having mass numbers 64 and 125 is ______.
- The radius of A1327A213227X nucleus is R. The radius of A53125A2532125Y nucleus will be ______.
- Answer the following question. Show that the density of the nucleus is independent of its mass number A.
- Using the Curve for the Binding Energy per Nucleon as a Function of Mass Number A, State Clearly How the Release in Energy in the Processes
- Write the Relationship Between the Size of a Nucleus and Its Mass Number (A)?
- A Heavy Nucleus X of Mass Number 240 and Binding Energy per Nucleon 7.6 Mev is Split into Two Fragments Y and Z of Mass Numbers 110 and 130. the Binding Energy of Nucleons in Y and Z is 8.5 Mev per
- Asha's mother read an article in the newspaper about a disaster that took place at Chernobyl. She could not understand much from the articles and asked a few questions from Asha regarding the article. Asha tried to answer her mother's questions based on what she learnt in Class XII Physics.
- Draw the Plot of Binding Energy per Nucleon (Be/A) as a Functino of Mass Number A. Write Two Important Conclusions that Can Be Drawn Regarding the Nature of Nuclear Force.
- In a Typical Nuclear Reaction, E.G. _1^2h+ 2 1 H → 3 2 H E + N + 3.27 Mev , Although Number of Nucleons is Conserved, Yet Energy is Released. How? Explain.
- Calculate the binding energy of an alpha particle in MeV. Given mass of a proton = 1.007825 u mass of a neutron = 1.008665 u mass of He nucleus = 4.002800 u 1u = 931 MeV/c2
- Write Symbolically the Nuclear β+ Decay Process
- Nucleus Formed in the Decay of the Nucleus is an Isotope Or Isobar
- Consider the fission of ""_92^238U by fast neutrons. In one fission event, no neutrons are emitted and the final end products,
- Define the Terms (I) Half-life (T1/2) and (Ii) Average Life (τ). Find Out Their Relationships with the Decay Constant (λ).
- Use this Graph to Explain the Release of Energy in Both the Processes of Nuclear Fusion and Fission.
- What Characteristic Property of Nuclear Force Explains the Constancy of Binding Energy per Nucleon (Be/A) in the Range of Mass Number ‘A’ Lying 30 < a < 170?
- Which Property of Nuclear Force Explains the Constancy of Binding Energy per Nucleon ( B E a ) for Nuclei in the Range 20< a < 170 ?
- The Figure Shows the Plot of Binding Energy (Be) per Nucleon as a Function of Mass Number A. the Letters A, B, C, D, and E Represent the Positions of Typical Nuclei on the Curve.
- Draw the Curve Showing the Variation of Binding Energy per Nucleon with the Mass Number of Nuclei. Using It Explain the Fusion of Nuclei Lying on Ascending Part and Fission
- Explain the release of energy in nuclear fission and fusion on the basis of binding energy per nucleon curve.
- Write two distinguishing features of nuclear forces.
- Draw a plot of potential energy of a pair of nucleons as a function of their separations. Mark the regions where the nuclear force is (i) attractive and (ii) repulsive.
- Determine the Distance of Closest Approach When an Alpha Particle of Kinetic Energy 4.5 Mev Strikes a Nucleus of Z = 80, Stops and Reverses Its Direction.
- Write the Basic Nuclear Process of Neutron Undergoing β-decay.
- Why is the Detection of Neutrinos Found Very Difficult?
- Write the Basic Nuclear Process Underlying β+ and β– Decays
- Write the β-decay of Tritium in Symbolic Form.
- Write Any Two Characteristic Properties of Nuclear Force.
- What is the Significance of Negative Sign in the Expression for the Energy?
- Complete the following nuclear reactions for α and β deca : (i) "_92^238U ->? + _2^4He + Q (ii) "_11^22Na ->? + _10^22Ne + v
- What is mass defect?
- How mass defect is related to the stability of the nucleus?
- Write Any Two Characteristic Features of Nuclear Forces ?
- Define the Term 'Decay Constant' of a Radioactive Sample. the Rate of Disintegration of a Given Radioactive Nucleus is 10000 Disintegrations/S and 5,000 Disintegrations/S After 20 Hr. and 30 Hr.
- Define 'Activity' of a Radioactive Substance ?
- Derive the mathematical expression for law of radioactive decay for a sample of a radioactive nucleus
- Identify the Nature of the Radioactive Radiations Emitted in Each Step of the Decay Process Given Below.
- Define one Becquerel.
- A radioactive substance disintegrates into two types of daughter nuclei, one type with disintegration constant λ1 and the other type with disintegration constant
- Write the Basic Nuclear Process Involved in the Emission of β+ in a Symbolic Form
- Why is It Found Experimentally Difficult to Detect Neutrinos in Nuclear β-decay?
- Write the Basic Nuclear Process Underlying this Decay
- Obtain the Relation Between the Decay Constant and Half Life of a Radioactive Sample.
- Why is It Experimentally Found Difficult to Detect Neutrinos in this Process ?
- How is the Mean Life of a Given Radioactive Nucleus Related to the Decay Constant?
- Define the Activity of a Given Radioactive Substance. Write Its S.I. Unit.
- In a Given Sample, Two Radioisotopes, a and B, Are Initially Present in the Ration of 1 : 4. the Half Lives of a and B Are Respectively 100 Years and 50 Years.
- Derive the Relation Between the Decay Constant and Half Life of a Radioactive Substance. a Radioactive Element Reduces to 25% of Its Initial Mass in 1000 Years. Find Its Half Life.
- Two Different Radioactive Elements with Half Lives T1 And T2 Have N1 And N2 Undecayed Atoms Respectively Present at a Given Instant.
- A Radioactive Nucleus 'A' Undergoes a Series of Decays as Given Below:
- A 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?
- A Radioactive Nucleus ‘A’ Undergoes a Series of Decays According to the Following Scheme:The Mass Number and Atomic Number of a Are 180 and 72 Respectively. What Are These Numbers for A4?
- The Radioactive Isotope D Decays According to the Sequenceif the Mass Number and Atomic Number of D2 Are 176 and 71 Respectively, What is (I) the Mass Number (Ii) Atomic Number of D?
Concepts [14]
- Atomic Masses and Composition of Nucleus
- Size of the Nucleus
- Mass - Energy
- Nuclear Binding Energy
- Nuclear Force
- Alpha Decay
- Beta Decay
- Gamma Decay
- Controlled Thermonuclear Fusion
- Nuclear Reactor
- Mass Defect and Binding Energy
- Atomic Mass, Mass - Energy Relation and Mass Defect
- Overview: Nuclei
- Law of Radioactive Decay
