Definitions [25]
A new type of neutral particle whose mass is very nearly the same as that of a proton is called neutron.
Nuclides with the same neutron number but different atomic number are called isotones.
All nuclides with the same mass number are called isobars.
A proton or a neutron is called a nucleon.
A different mass unit used for expressing atomic masses is the atomic mass unit (u), defined as one-twelfth of the mass of a carbon-12 atom, called atomic mass unit.
Mathematically: 1 u = \[\frac{\text{mass of one }^{12}\mathrm{C~atom}}{12}\] = 1.660539 × 10−27 kg
Atomic species of the same element differing in mass are called isotopes.
The nucleus of the lightest atom of hydrogen, which has a relative abundance of 99.985%, is called the proton.
The nuclear radius is the effective distance from the centre of the nucleus to its outer boundary. Since the nucleus does not have a perfectly sharp surface, this radius is treated as an approximate effective value in physics.
Binding energy per nucleon is the average binding energy associated with each nucleon in the nucleus.
The binding energy of a nucleus is the minimum energy required to separate the nucleus completely into its constituent protons and neutrons.
Mass defect is the difference between:
- the sum of the masses of the constituent protons and neutrons, and
- the actual mass of the nucleus.
The nuclear force is the strong attractive force between nucleons (protons and neutrons) that binds them together inside the nucleus.
Define free electrons.
Electrons in outer orbits are weakly bound with the nucleus. In solids these weakly bound electrons leave their individual atom and become a part of it. These electrons are known as free electrons.
Define bound electrons.
As nucleus is positively charged it strongly attracts the negative charged electrons. The electron orbit close to the nucleus are tightly bound by strong attractive force of nucleus. These electrons are known as bound electrons.
Define the term radioactivity.
The phenomenon of spontaneous disintegration of an unstable nucleus of a naturally occurring isotope accompanied by emission of active radiations, α particles, β particles and γ radiations is called radioactivity.
Radioactivity is the spontaneous emission of high-energy radiation from the nucleus of an unstable atom.
A radioactive substance is a substance whose nuclei are unstable and therefore emit radiation on their own.
Energy is released when nuclei undergo reactions (fission or fusion) that move them from a state of lower total binding energy to a state of higher total binding energy.
The splitting of a heavy nucleus into lighter nuclei, releasing energy.
The combination of light nuclei to form a heavier nucleus, releasing energy.
Nuclear fission is a neutron-induced nuclear reaction in which a heavy nucleus, such as uranium-235, breaks into two intermediate-mass nuclear fragments.
Nuclear fusion is the process in which light nuclei combine to form a more tightly bound heavier nucleus, and energy is released during the process.
Because both nuclei carry a positive charge, they repel each other through electrostatic force. This repulsion is called the Coulomb barrier in the context of fusion.
Thermonuclear fusion is fusion initiated by extremely high temperature, which gives nuclei enough kinetic energy to approach one another closely.
Controlled thermonuclear fusion is the attempt to produce this fusion process under controlled conditions on Earth so that the released energy can be used safely and continuously.
Formulae [8]
mp = 1.00727 u = 1.67262 × 10−27 kg
mn = 1.00866 u = 1.6749 × 10−27 kg
A = Z + N
Where:
- Z = atomic number = number of protons.
- N = neutron number = number of neutrons.
- A = mass number = total number of protons and neutrons.
The experimentally observed relation is: R = R0A1/3
where:
- R = radius of the nucleus
- R0 = radius constant
- A = mass number of the nucleus.
For nuclei,
-
R0 ≈ 1.2 × 10−15 m.
Einstein gave the famous mass-energy equivalence relation:
Where:
- E = energy equivalent of mass mm
- m = mass
- c = velocity of light in vacuum
- c ≈ 3 × 108 m s−1
\[\Delta M=[Zm_p+(A-Z)m_n]-M\]
Where:
- ΔM = mass defect
- mp = mass of one proton
- mn = mass of one neutron
- M = actual mass of the nucleus
Eb = ΔMc2
Where:
- Eb = binding energy
- ΔM = mass defect
- c = speed of light
\[E_{bn}=\frac{E_b}{A}\]
Where:
- Ebn = binding energy per nucleon
- Eb = total binding energy of the nucleus
- A = mass number
Important Questions [26]
- Show that the Density of Nucleus Over a Wide Range of Nuclei is Constant-independent of Mass Number A.
- 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.
- 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.
- Two nuclei have different mass numbers A1 and A2. Are these nuclei necessarily the isotopes of the same element? Explain.
- Calculate the Released Energy.
- Two nuclei may have the same radius, even though they contain different numbers of protons and neutrons. Explain.
- Two Nuclei Have Mass Numbers in the Ratio 1: 2. What is the Ratio of Their Nuclear Densities?
- Distinguish between isotopes and isobars.
- 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
- 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.
- 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.
- 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.
- 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
- 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.
- A heavy nucleus P of mass number 240 and binding energy of 7.6 MeV per nucleon splits into two nuclei Q and R of mass number 110 and 130 and binding energy per nucleon of 8.5 MeV and 8.4 MeV
- Distinguish between nuclear fission and fusion giving an example of each.
- The curve of binding energy per nucleon as a function of atomic mass number has a sharp peak for helium nucleus. This implies that helium nucleus is ______.
- In a Nuclear Reaction 3 2 H E + 3 2 H E → 4 2 H E + 1 1 H + 1 1 H + 12.86 M E V Though the Number of Nucleons is Conserved on Both Sides of the Reaction, Yet the Energy is Released. How? Explain.
- Distinguish Between Nuclear Fission and Fusion.
- Calculate the Energy in Fusion Reaction
- Explain the Processes of Nuclear Fission and Nuclear Fusion by Using the Plot of Binding Energy per Nucleon (Be/A) Versus the Mass Number a
