- In nuclear fission of U‑235, a slow neutron is absorbed to form unstable U‑236, which splits into two nuclei with the release of three neutrons and energy.
- Energy released in fission is due to loss of mass, and is given by Einstein’s mass‑energy relation, E = (Δm)c2.
- In each fission reaction, atomic number (Z) and mass number (A) remain conserved, though mass is converted into energy.
- Fission of one U‑235 nucleus releases nearly 190 MeV energy, mainly as kinetic energy of fragments, neutrons, γ‑rays, heat, and light.
Definitions [33]
Define the term atomic number.
The number of protons in the nucleus is known as the atomic number of the element and is denoted by Z.
The number of protons in the nucleus of an atom, which is characteristic of a chemical element and determines its place in the periodic table. Atomic number is also equal to the number of electrons in an atom.
Define the term mass number.
The total number of neutrons and protons in the nucleus is called the mass number of the element and is denoted by A.
Definition: Mass Number
The mass number of an atom is equal to the total number of nucleons (i.e., the sum of the number of protons and the number of neutrons) in its nucleus.
Definition: Atomic Number
The atomic number of an atom is equal to the number of protons in its nucleus (which is same as the number of electrons in a neutral atom).
Definition: Excitation Energy
The energy required to take an electron from the ground state to an excited state is called the Excitation Energy of the electron in that state.
Definition: Energy Levels
The definite amount of energies associated with the electrons in different orbits of an atom are called the Energy Levels (of that atom).
Define the term Nucleons.
The nucleus is made up of protons and neutrons, with protons having a positive charge and neutrons being neutral. Nucleons are made up of protons and neutrons.
Definition: Binding Energy
The energy equivalent to that of mass defect, i.e., the energy required for holding the nucleons together in a nucleus, is called the Binding Energy of the nucleus.
Definition: Binding Energy Per Nucleon
The ratio of the binding energy Eb of a nucleus to the number of nucleons A in that nucleus is called Binding Energy Per Nucleon.
Definition: Energy Levels
The definite amount of energies associated with the electrons in different orbits of an atom are called the Energy Levels (of that atom).
Definition: Excitation Energy
The energy required to take an electron from the ground state to an excited state is called the Excitation Energy of the electron in that state.
Definition: Binding Energy of Electron
The minimum energy required to make an electron free from the nucleus is called the Binding Energy of an electron.
Definition: Ionization Energy
The minimum amount of energy required to be given to an electron in the ground state of an atom to set the electron free is called the Ionization Energy of that atom.
Definition: β-Decay
The spontaneous emission of an electron (β⁻-decay) or a positron (β⁺-decay) from a radioactive nucleus is called β-Decay.
Definition: Radioactive Decay
The nuclear phenomenon in which an unstable nucleus undergoes decay with the emission of some particles (α, β) and electromagnetic radiation (γ-rays) is called Radioactive Decay.
Definition: Activity
The rate of decay, i.e., the number of decays per unit time \[\left(-\frac{dN(t)}{dt}\right)\], is called Activity A(t).
Definition: Average Life
The arithmetic average of the lives of all the nuclei present initially is called the Average Life of a radioactive element.
Definition: Half-Life
The time in which half the substance (radioactive) is disintegrated is called the Half-Life Period of a radioactive substance.
Definition: α-Decay
The phenomenon of emission of a nucleus of helium (2He4) from a radioactive nucleus is called α-Decay.
Define half-life period.
The half-life of a reaction is the time it takes for a reactant’s concentration to decrease to half of its initial value.
Definition: γ-Decay
When a nucleus in an excited state spontaneously decays to its ground state and a photon is emitted with energy equal to the difference in the two energy levels of the nucleus, this is called γ-Decay.
Definition: Q-Value
The difference in the energy equivalent of the mass of the parent atom and that of the sum of masses of the products is called the Q-Value of the decay.
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.
Definition: Nuclear Energy
The energy released due to loss in mass during the processes of nuclear fission and fusion is called nuclear (or atomic) energy.
OR
The energy released when nuclei undergo a nuclear reaction (change in structure, forming new nuclei) is called nuclear energy.
OR
The energy released during the transformation of nuclei is called Nuclear Energy.
Definition: Mass Defect
The difference between the sum of the masses of the nucleons composing a nucleus and the rest mass of the nucleus is called the mass defect.
Definition: Nuclear Fission
Nuclear fission is the process in which a heavy nucleus splits into two lighter nuclei of nearly the same size, when bombarded with slow neutrons. In each fission reaction, a tremendous amount of energy (≈ 190 MeV) is released.
OR
The process of splitting of a heavy nucleus (92U235 or 92U239) into two lighter nuclei of comparable masses along with the release of a large amount of energy after being bombarded by slow neutrons is called Nuclear Fission.
Definition: Nuclear Fusion
Nuclear fusion is the process in which two light nuclei combine to form a heavy nucleus. In this process also, huge amount of energy is released.
OR
The phenomenon in which two light nuclei fuse to form a larger nucleus and energy is released is called Nuclear Fusion.
Definition: Hydrogen Spectrum
The collection of different spectral lines obtained due to transition of an electron in hydrogen atom from upper energy levels to lower energy levels is called the Hydrogen Spectrum.
Definition: Emission Line Spectrum
The spectrum consisting of bright lines on a dark background, emitted when an atomic gas is excited at low pressure by passing an electric current through it, is called the Emission Line Spectrum.
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.
Definition: Radioactivity
Radioactivity is a nuclear phenomenon. It is the process of spontaneous emission of α or β and γ radiations from the nucleus of atoms during their decay.
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 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.
Formulae [6]
Formula: Bohr's Angular Momentum
L = \[\frac {nh}{2π}\]
Formula: Binding Energy
Eb = ΔM ⋅ c2
Eb = [(Zmp + (A − Z)mn) − M] × c2
Formula: Binding Energy per Nucleon
Ebn = \[\frac {E_b}{A}\]
Formula: Q-Value (general)
Q = [Mparent − Mproducts]c2
Formula: Q-value of α-decay
Q = [mX − mY − mHe]c2
Formula: Q-value of β-decay
Q = [mX − mY − me]c2
Theorems and Laws [3]
The ground state energy of the hydrogen atom is -13.6 eV. The kinetic and potential energy of the electron in the second excited state is respectively ______
The ground state energy of the hydrogen atom is -13.6 eV. The kinetic and potential energy of the electron in the second excited state is respectively 1.51 eV, -3.02 eV.
Explanation:
For second excited state n = 3
The total energy in the third orbit
`E_3 = (-13.6)/9`eV = -1.51 eV
K.E. = -T.E. = 1.51 eV
P.E. = 2.T.E. = -3.32 eV
Law: Bohr's Postulates
- An electron in an atom revolves round the nucleus in a fixed circular orbit (stationary orbit) with constant speed without emitting radiant energy. Thus each atom has definite states and each possible state has definite total energy.
- The electron revolves around the nucleus only in those orbits for which the angular momentum is an integral multiple of h2π2πh, where hh is Planck's constant (6.6 × 10-34 J·s). Thus the angular momentum is quantised:
L = \[\frac{nh}{2π}\] - An electron can make a transition from a higher unstable orbit to a lower stable orbit. When it does so, a photon is emitted having energy equal to the energy difference between the initial and final states. The frequency of the emitted photon is:
v = \[\frac {E_i−E_f}{h}\]
where Ei and Ef are the energies of the initial and final states and Ei > Ef. - Failures of Bohr's Model: It is unable to explain the fine structure of spectral lines and is valid only for single-electron atoms.
Law: Radioactive Decay
- The law states that the rate at which a radioactive substance undergoes decay is directly proportional to the number of undecayed nuclei present in the sample.
- Mathematically: \[\frac {dN}{dt}\] ∝ N, which gives \[\frac {dN}{dt}\] = −λN, where λ is the decay constant.
- On solving, the number of undecayed nuclei at time t is:
N(t) = N0e−λt
where N0 is the number of nuclei present initially. - The time taken for the number of parent radioactive nuclei to reduce to half its value is called the half-life of the species, and the average life of a radioactive species is the average time a nucleus survives before it decays.
Key Points
Key Points: Structure of the Atom and Nucleus
- The structure of an atom and its nucleus was developed from the discovery of electrons by J.J. Thomson and alpha particle scattering experiments by Rutherford.
- An atom consists of electrons, protons, and neutrons, with protons and neutrons in the nucleus and electrons revolving in stationary orbits.
- The maximum number of electrons in a shell is given by 2n², and the shells are named K, L, M, N, O, P, and Q.
Key Points: Lord Rutherford’s Atomic Model
- Proposed by Ernest Rutherford in 1911 based on the gold foil (α-particle scattering) experiment.
- Most α-particles passed straight through, showing that the atom is mostly empty space.
- Some α-particles were deflected, indicating the presence of a positively charged centre.
- Very few α-particles were deflected at large angles or bounced back, proving a dense nucleus.
- All the positive charge and most of the mass are concentrated in a tiny nucleus (~10⁻¹⁵ m).
- Electrons revolve around the nucleus in circular orbits.
- The electrostatic force of attraction between nucleus and electrons keeps them in orbit.
- Limitation: Could not explain stability of atom and line spectra of hydrogen.
Key Points: Limitations of Bohr’s Model
- Could not explain the fine structure (splitting) of the spectral lines of hydrogen.
- Failed to explain the spectra of multi-electron atoms.
- Could not explain the splitting of spectral lines in a magnetic field (Zeeman effect) and an electric field (Stark effect).
- Failed to explain the formation of molecules and chemical bonding.
- Inconsistent with Heisenberg’s Uncertainty Principle.
- Could not explain the intensity of spectral lines.
Key Points: de Broglie's Dual Nature of Matter
Moving particles (like electrons) behave both as particles and as waves:
\[\lambda=\frac{h}{mv}=\frac{h}{p}\]
where p = mv = momentum of the particle.
Key Points: Nuclear Fission
Key Points: Dalton's Atomic Theory
Dalton's atomic theory laid the foundation of modern chemistry with four core postulates:
- All matter is made up of extremely small particles called atoms.
- Atoms of the same element are identical to each other in mass and properties; atoms of different elements differ.
- Atoms can neither be created nor destroyed — they are indestructible.
- Atoms combine in fixed, simple whole-number ratios to form compound atoms (molecules).
Note: Modern discoveries have refined some postulates (e.g., isotopes show atoms of the same element can differ in mass), but the core framework remains foundational.
Concepts [20]
- Structure of the Atom and Nucleus
- Thomson’s Atomic Model
- Geiger-marsden Experiment
- Lord Rutherford’s Atomic model
- Atomic Spectra
- Bohr’s Atomic Model
- Radii of the Orbits
- Energy of the Electrons
- Limitations of Bohr's Model
- De Broglie's Explanation
- Atomic Nucleus
- Nuclear Binding Energy
- Radioactive Decays
- Law of Radioactive Decay
- Forms of Energy > Nuclear Energy
- Nuclear Fission
- Nuclear Fusion
- Dalton's Atomic Theory
- Hydrogen Spectrum
- Radioactivity
