ISC Class 12 Physics Syllabus 2023-24

(i) Electric Charges and Fields

 Electric charges; conservation and quantisation of charge, Coulomb's law; superposition principle and continuous charge distribution. Electric field, electric field due to a point charge, electric field lines, electric dipole, electric field due to a dipole, torque on a dipole in uniform electric field.
Electric flux, Gauss’s theorem in Electrostatics and its applications to find field due to infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell.

(a) Coulomb's law, S.I. unit of charge; permittivity of free space and of deielectric medium. Frictional electricity, electric charges (two types); repulsion and attraction; simple atomic structure -electrons and ions; conductors and insulators; quantization and conservation of electric charge; Coulomb's law in vector from; (position coordinates r1, r2 not necessary). Comparison with Newton's law of gravitation; Superposition principle $$(\vec{F}_1=\vec{F}_{12}+\vec{F}_{13}+\vec{F}_{14}+...).$$

 (b) Concept of electric field and its intensity; examples of different fields; gravitstional, electric and magnetic; Electric field due to a point charge $$\vec{E}=\vec{F}/q_0 $$ (q0 is a test charge); $$\vec{E}$$ for a group of charges (superposition principle); a point charge q in an electric field

$$\vec{E}$$ experiences an electric force $$\vec{F}_E=q\vec{E}$$. Intensity due to a continuous distribution of charge i.e. linear, surface and volume.

(c) Electric lines of force; A conventent way to visualize the electric field; properties of lines of force; examples of the lines of force due to (i) an isolated point charge (+ve and -ve); (ii) dipole, (ii) two similar charges of a small distance;(iv) uniform field between two oppositely charged parallel plates.

 (d) Electric dipole and dipole moment; derivation of the $$\vec{E}$$ at a point, (1) on the perpendicular bisector (equatorial i.e. broad side on position) of a dipole , also for r >> 21 (short dipole); dipole in a uniform electric field; net force zero, torque on an electric dipole: $$\vec\tau=\vec p×\vec E$$ and its derivation.

(a) Concept of potential, potential difference and potential energy. Equipotential surface and its properties. Obtain an expression for electric potential at a point due to a point charge; graphical variation of E and V vs r, V_p=W/q₀; hence V_A-V_B= W_BA/q0 (taking q₀ from B to A) = (q=4πε₀)(1/r_A-1/r_B); derive this equation; also V_A=q/4πε₀.1/r_A; for q>0, V_A>0 and for q <0, V_A < 0. For a collection of charges V = algebraic sum of the potentials due to each charge;
potential due to a dipole on its axial line and equatorial line; also at any point for r > >2l (short dipole). Potential energy of a point charge (q) in an electric field$$\vec E$$, placed at a point P where potential is V, is given by U=_qV and ΔU=q(V_A-V_B).
The electrostatic potential energy of a system of two charges = work done W₂₁=W₂₁ in assembling the system; U₁₂ or U₂₁= (1/4πε₀) q₁q₂/r₁₂. For a system of 3 charges U₁₂₃=U₁₂+U₁₃+ U₂₃ $$=\frac{1}{4\pi\epsilon_0}(\frac{q_1q_2}{r_{12}}+\frac{q_1q_3}{r_{13}}+\frac{q_2q_3}{r_{23}}).$$ For a dipole in a uniform electric field , derive an expression of the electric potential energy $$\text{U}_{E}=-\vec{P}.\vec{E},$$ special cases for Φ=0°, 90°, 180°

(b) Capacitance of a conductor C= Q/V; obtain the capacitance of a parallel-plate capacitor (C= ∈₀A/d) and equivalent capacitance for capacitors in series and parallel combinations. Obtain an $$\text{expression for energy stored}\\(U=\frac{1}{2}CV^{2}=\frac{1}{2}\text{QV}=\frac{1}{2}\frac{Q^{2}}{C})\\\text{and energy density.}$$

(c) Dielectric constant K= C'/C; this is also called relative permittivity K= ∈_r= ∈/∈₀ ; elementory ideas of polarization of matter in a uniform electric field qualitative discussion; induced surface charges weaken the original field; results in reduction in $$\vec{E}$$ and hence, in pd, (V); for charge remaining the same Q = CV = C'V'= K. CV'; V' = V/K; and $$E'=\frac{\text{E}}{K};$$ if the Capacitor is kept connected with the source of emf, V is kept constant V = Q/C = Q'/C' ; Q'=C'V = K. CV= K. Q increases; For a parallel plate capacitor with a dielectric in between, C' = KC = K.∈o . A/d = ∈r .∈o .A/d.
$$ \text{Then}\space C'=\frac{∈_0A}{\frac{d}{∈_r}};$$ for a capacitor partially filled dielectric, capacitance, C' =∈_oA/(d-t + t/∈_r).

(a) Free electron theory of conduction; acceleration of free electrons, relaxation time τ ; electric current I = Q/t; concept of drift velocity and electron mobility. Ohm's law, current density J = I/A; experimental verification, graphs and slope, ohmic and non-ohmic conductors; obtain the relation I=v_denA. Derive σ = ne² τ/m and ρ = m/ne² τ ; effect of temperature on resistivity and resistance of conductors and semiconductors and graphs. Resistance R= V/I; resistivity ρ, given by R = ρ.l/A; conductivity and conductance; Ohm’s law as $$\vec{J}=\sigma\vec{E}; $$ colour coding of resistance. 

(b) Electrical energy consumed in time t is E=Pt= VIt; using Ohm’s law $$\text{E}=\bigg(\frac{V^{2}}{R}\bigg)t= I^{2}\text{Rt}.$$ Potential difference V = P/ I; P = V I; Electric power consumed P = VI = V² /R = I² R; commercial units; electricity consumption and billing. Derivation of equivalent resistance for combination of resistors in series and parallel; special case of n identical resistors; R_s = nR and R_p = R/n. Calculation of equivalent resistance of mixed grouping of resistors (circuits).

(c) The source of energy of a seat of emf (such as a cell) may be electrical, mechanical, thermal or radiant energy. The emf of a source is defined as the work done per unit charge to force them to go to the higher point of potential (from -ve terminal to +ve terminal inside the cell) so, ε = dW /dq; but dq = Idt; dW = εdq = εIdt . Equating total work done to the work done across the external resistor R plus the work done across the internal resistance r; εIdt=I² R dt + I² rdt; ε =I (R + r); I=ε/( R + r ); also IR +Ir = ε or V=ε- Ir where Ir is called the back emf as it acts against the emf ε; V is the terminal pd. Derivation of formulae for combination for identical cells in series, parallel and mixed grouping. Parallel combination of two cells of unequal emf. Series combination of n cells of unequal emf

(d) Statement and explanation of Kirchhoff's laws with simple examples. The first is a conservation law for charge and the 2^nd is law of conservation of energy. Note change in potential across a resistor ∆V=IR<0 when we go ‘down’ with the current (compare with flow of water down a river), and ∆V=IR>0 if we go up against the current across the resistor. When we go through a cell, the -ve terminal is at a lower level and the +ve terminal at a higher level, so going from -ve to +ve through the cell, we are going up and ∆V=+ε and going from +ve to -ve terminal through the cell, we are going down, so ∆V = -ε. Application to simple circuits. Wheatstone bridge; right in the beginning take I_g=0 as we consider a balanced bridge, derivation of R₁/R₂ = R₃/R₄ [Kirchhoff’s law not necessary]. Metre bridge is a modified form of Wheatstone bridge, its use to measure unknown resistance. Here R₃ = l₁ρ and R₄=l₂ρ; R₃R₄=l₁/l₂. Principle of Potentiometer: fall in potential ∆V α ∆l; auxiliary emf ε₁ is balanced against the fall in potential V₁ across length l₁. ε₁ = V₁ =Kl₁ ; ε₁/ε₂ = l₁/l₂; potentiometer as a voltmeter. Potential gradient and sensitivity of potentiometer. Use of potentiometer: to compare emfs of two cells, to determine internal resistance of a cell.

(a) Only historical introduction through Oersted’s experiment. [Ampere’s swimming rule not included]. Biot-Savart law and its vector form; application; derive the expression for B (i) at the centre of a circular loop carrying current; (ii) at any point on its axis. Current carrying loop as a magnetic dipole. Ampere’s Circuital law: statement and brief explanation. Apply it to obtain $$\vec{B}$$near a long wire carrying current and for a solenoid (straight as well as torroidal). Only formula of $$\vec{B}$$ due to a finitely long conductor.

(b) Force on a moving charged particle in magnetic field $$\vec{F}_B=q(\vec{v}×\vec{B});$$ special cases, modify this equation substituting $$\frac{d\vec{l}}{dt}\space\text{for v and I for q/dt to yield}\space\vec{F}=Id\vec{B}$$ for the force acting on a current carrying conductor placed in a magnetic field. Derive the expression for force between two long and parallel wires carrying current, hence, define ampere (the base SI unit of current) and hence, coulomb; from Q = It. Lorentz force, Simple ideas about principle, working, and limitations of a cyclotron

(c) Derive the expression for torque on a current carrying loop placed in a $$\text{uniform}\space\vec{B}, \text{ using}\space\vec{F}=I\vec{l}×\vec{B}\text{and}\space\vec\tau=\vec r×\vec F;\tau=\text{NIAB sinφ for N turns}\\\vec{\tau} =\vec{m}×\vec{B},\text{where the dipole moment}\\\vec{m}=\text{NI}\vec{A},$$ unit: A.m² . A current carrying loop is a magnetic dipole; directions of current and $$\vec{B} \text{and}\space\vec{m}$$ using right hand rule only; no other rule necessary. Mention orbital magnetic moment of an electron in Bohr model of H atom. Concept of radial magnetic field. Moving coil galvanometer; construction, principle, working, theory I= kφ , current and voltage sensitivity. Shunt. Conversion of galvanometer into ammeter and voltmeter of given range

(d) Magnetic field represented by the symbol $$\vec{B}\space\text{is now defined by the equation}$$ $$\vec{F}=q_0(\vec{v}×\vec{B});\vec{B}\space\\\text{is not to be defined in terms of force acting on a unit pole, etc.; note the distinction of}\\ \vec{B}\space\text{from} \vec{E}\text{is that}\space\vec{B}\text{forms closed loops as there are no magnetic monopoles, whereas }\\ \vec{E} \text{lines start from +ve charge and end on -ve charge. Magnetic field lines due to a magnetic dipole (bar magnet).}\\\text{ Magnetic field in end-on and broadside-on positions (No derivations). Magnetic flux }\\\phi=\vec{B}\vec{A}=\text{BA for B uniform and}\\\vec{B}||\vec{A};\text{i.e. area held perpendicular to For}\\ \phi\text{BA}(\vec{B}||\vec{A}),$$
$$\vec{B}=\phi/A\text{is the flux density [SI unit of flux is weber (Wb)]; but note} \\\text{that this is not correct as a defining equation as}\\ \vec{B}\text{is vector and φ and φ/A are scalars, unit of B is tesla (T) equal to} 10^{-4}\\ \text{gauss. For non-uniform B field, φ}=\int d\phi=\int \vec{B}.d\vec{A}.\\\text{Earth's magnetic field }=\vec{B}_E \text{is uniform over a limited arealike that of a lab; the component of this field in the horizontal direction B}_H \\\text{is the one effectively acting on a magnet suspended or pivoted horizontally. Elements of earth’s magnetic field, i.e.} \\B_H, δ and θ - \text{their definitions and relations}$$

(e) Properties of diamagnetic, paramagnetic and ferromagnetic substances; their susceptibility and relative permeability. It is better to explain the main distinction, the cause of magnetization (M) is due to magnetic dipole moment (m) of atoms, ions or molecules being 0 for dia, >0 but very small for para and > 0 and large for ferromagnetic materials; few examples; placed in external $$\vec{B}\space\text{, very small (induced) magnetization in a direction opposite to}\\\vec{B}\space\text{in dia, small magnetization parallel to}\\\vec{B}\space\text{for para, and large magnetization parallel to}\\\vec{B}\space\text{for ferromagnetic materials; this leads to lines of}\space\vec{B}$$ becoming less dense, more dense and much more dense in dia, para and ferro, respectively; hence, a weak repulsion for dia, weak attraction for para and strong attraction for ferro magnetic material. Also, a small bar suspended in the horizontal plane becomes perpendicular to the $$\vec{B}\space\text{field for dia and parallel to} \vec{B}$$ for para and ferro. Defining equation H = (B/µ0)-M; the magnetic properties, susceptibility χm = (M/H) < 0 for dia (as M is opposite H) and > 0 for para, both very small, but very large for ferro; hence relative permeability µr =(1+ χm) < 1 for dia, > 1 for para and >>1 (very large) for ferro; further, χm∝1/T (Curie’s law) for para, independent of temperature (T) for dia and depends on T in a complicated manner for ferro; on heating ferro becomes para at Curie temperature. Electromagnet: its definition, properties and factors affecting the strength of electromagnet; selection of magnetic material for temporary and permanent magnets and core of the transformer on the basis of retentivity and coercive force (B-H loop and its significance, retentivity and coercive force not to be evaluated).

(i) Electromagnetic Induction

Faraday's laws, induced emf and current; Lenz's Law, eddy currents. Self-induction and mutual induction. Transformer.

(ii) Alternating Current 

Peak value, mean value and RMS value of alternating current/voltage; their relation in sinusoidal case; reactance and impedance;  

(a) Electromagnetic induction, Magnetic flux, change in flux, rate of change of flux and induced emf; Faraday’s laws. Lenz's law, conservation of energy; motional emf ε = Blv, and power P = (Blv) ²/R; eddy currents (qualitative); 

(b) Self-Induction, coefficient of selfinductance, $$\phi=\text{LI and L}=\frac{\epsilon}{\frac{dl}{dt}};$$ henry = volt. Second/ampere, expression for coefficient of self-inductance of a solenoid $$\text{L}=\frac{\mu_0N^{2}A}{l}=\mu_0n^{2} A×l.$$ Mutual induction and mutual inductance (M), flux linked φ₂ = MI₁; induced emf $$\epsilon_2=\frac{d\phi_2}{dt}=M\frac{dI_1}{dt}.\text{Definition of M as }\\\text{M}=\frac{\epsilon_2}{\frac{dI_1}{dt}}\text{or M}=\frac{\phi_2}{I_1}.\\ \text{SI unit henry. Expression for coefficient of mutual inductance of two coaxial solenoids.}\\ \text{M}=\frac{\mu_0N_1N_2A}{l}=\mu_0n_1N_2A$$ Induced emf opposes changes, back emf is set up, eddy currents. Transformer (ideal coupling): principle, working and uses; step up and step down; efficiency and applications including transmission of power, energy losses and their minimisation.

 (c) Sinusoidal variation of V and I with time, for the output from an ac generator; time period, frequency and phase changes; obtain mean values of current and voltage, obtain relation between RMS value of V and I with peak values in sinusoidal cases only.

(d) Variation of voltage and current in a.c. circuits consisting of only a resistor, only an inductor and only a capacitor (phasor representation), phase lag and phase lead. May apply Kirchhoff’s law and obtain simple differential equation (SHM type), V = Vo sin ωt, solution I = I0 sin ωt, I0sin (ωt + π/2) and I0 sin (ωt - π/2) for pure R, C and L circuits respectively. Draw phase (or phasor) diagrams showing voltage and current and phase lag or lead, also showing resistance R, inductive reactance X_L; (X_L=ωL) and capacitive reactance X_C, (X_C = 1/ωC). Graph of X_L and X_C vs f

(e) The LCR series circuit: Use phasor diagram method to obtain expression for I and V, the pd across R, L and C; and the net phase lag/lead; use the results of 4(e), V lags I by π/2 in a capacitor, V leads I by π/2 in an inductor, V and I are in phase in a resistor, I is the same in all three; hence draw phase diagram, combine V_L and V_c (in opposite phase; phasors add like vectors) to give V=V_R+V_L+V_C (phasor addition) and the max. values are related by V² _m=V² _Rm+(V_Lm-V_Cm)² when V_L>V_C Substituting pd=current x resistance or reactance, we get Z² =R² +(X_L-X_c) ² and tanφ = (V_{L m} -V_Cm)/V_Rm = (X_L-X_c)/R giving I = I _m sin (wt-φ) where I _m =V_m/Z etc. Special cases for RL and RC circuits. [May use Kirchoff’s law and obtain the differential equation] Graph of Z vs f and I vs f

(f) Power P associated with LCR circuit = $$\frac{1}{2}V_0I_0\text{cos}\phi= V_{rms}I_{rms}\space\text{cos} \phi=I rms^{2} R;\\\text{power absorbed and power dissipated; electrical resonance; bandwidth of signals}\\\text{ and Q factor (no derivation); oscillations in an LC circuit}(\omega_0=\frac{1}{\sqrt{LC}})\\\text{Average power consumed averaged over a full cycle}\\\bar{P}=(1/2)\space V_0I_0\space cos\phi,$$ Power factor cosφ = R/Z. Special case for pure R, L and C; choke coil (analytical only), X_L controls current but cosφ = 0, hence $$\bar{P}=0 \text{wattless current; LC circuit; at resonance with} X_L=X_c , Z=Z_{min}= R,\\\text{ power delivered to circuit by the source is maximum, resonant frequency}\\f_0=\frac{1}{2\pi\sqrt{LC}}.$$

(g) Simple a.c. generators: Principle, description, theory, working and use. Variation in current and voltage with time for a.c. and d.c. Basic differences between a.c. and d.c.

(i) Ray Optics and Optical Instruments

Ray Optics: Reflection of light by spherical mirrors, mirror formula, refraction of light at plane surfaces, total internal reflection and its applications, optical fibres, refraction at spherical surfaces, lenses, thin lens formula, lens maker's formula, magnification, power of a lens, combination of thin lenses in contact, combination of a lens and a mirror, refraction and dispersion of light through a prism. Scattering of light. 

Optical instruments: Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers and their resolving powers. 

(a) Reflection of light by spherical mirrors. Mirror formula: its derivation; R=2f for spherical mirrors. Magnification.

(b) Refraction of light at a plane interface, Snell's law; total internal reflection and critical angle; total reflecting prisms and optical fibers. Total reflecting prisms: application to triangular prisms with angle of the prism 30° , 45° , 60° and 90° respectively; ray diagrams for Refraction through a combination of media, ₁n₂× ₂n₃× ₃n₁=1, real depth and apparent depth. Simple applications

(c) Refraction through a prism, minimum deviation and derivation of relation between n, A and δ_min. Include explanation of i-δ graph, i₁ = i₂ = i (say) for δ_m; from symmetry r₁ = r₂; refracted ray inside the prism is parallel to the base of the equilateral prism. Thin prism. Dispersion; Angular dispersion; dispersive power, rainbow - ray diagram (no derivation). Simple explanation. Rayleigh’s theory of scattering of light: blue colour of sky and reddish appearance of the sun at sunrise and sunset clouds appear white.

(d) Refraction at a single spherical surface; detailed discussion of one case only - convex towards rarer medium, for spherical surface and real image. Derive the relation between n₁, n₂, u, v and R. Refraction through thin lenses: derive lens maker's formula and lens formula; derivation of combined focal length of two thin lenses in contact. Combination of lenses and mirrors (silvering of lens excluded) and magnification for lens, derivation for biconvex lens only; extend the results to biconcave lens, plano convex lens and lens immersed in a liquid; power of a lens P=1/f with SI unit dioptre. For lenses in contact 1/F= 1/f₁+1/f₂ and P=P₁+P₂. Lens formula, formation of image with combination of thin lenses and mirrors.
[Any one sign convention may be used in solving numericals].

(e) Ray diagram and derivation of magnifying power of a simple microscope with image at D (least distance of distinct vision) and infinity; Ray diagram and derivation of magnifying power of a compound microscope with image at D. Only expression for magnifying power of compound microscope for final image at infinity.
Ray diagrams of refracting telescope with image at infinity as well as at D; simple explanation; derivation of magnifying power; Ray diagram of reflecting telescope with image at infinity. Advantages, disadvantages and uses. Resolving power of compound microscope and telescope.

(ii) Wave Optics

Wave front and Huygen's principle. Proof of laws of reflection and refraction using Huygen's principle. Interference, Young's double slit experiment and expression for fringe width(β), coherent sources and sustained interference of light, Fraunhofer diffraction due to a single slit, width of central maximum, polarisation, plane polarised light, Brewster's law, uses of plane polarised light and Polaroids. 

(a) Huygen’s principle: wavefronts - different types/shapes of wavefronts; proof of laws of reflection and refraction using Huygen’s theory. [Refraction through a prism and lens on the basis of Huygen’s theory not required]. 

(b) Interference of light, interference of monochromatic light by double slit. Phase of wave motion; superposition of identical waves at a point, path difference and phase difference; coherent and incoherent sources; interference: constructive and destructive, conditions for sustained interference of light waves [mathematical deduction of interference from the equations of two progressive waves with a phase difference is not required]. Young's double slit experiment: set up, diagram, geometrical deduction of path difference ∆x = dsinθ, between waves from the two slits; using ∆x=nλ for bright fringe and ∆x= (n+½)λ for dark fringe and sin θ = tan θ =y_n /D as y and θ are small, obtain y_n=(D/d)nλ and fringe width β=(D/d)λ. Graph of distribution of intensity with angular distance.

(c) Single slit Fraunhofer diffraction (elementary explanation only). Diffraction at a single slit: experimental setup, diagram, diffraction pattern, obtain expression for position of minima, a sinθn= nλ, where n = 1,2,3… and conditions for secondary maxima, asinθn =(n+½)λ.; distribution of intensity with angular distance; angular width of central bright fringe. 

(d) Polarisation of light, plane polarised electromagnetic wave (elementary idea only), methods of polarisation of light. Brewster's law; polaroids. Description of an electromagnetic wave as transmission of energy by periodic changes in $$\vec{E}\space\text{and}\space\vec{B}\space\text{along the path; transverse nature as}\\\vec{E}\space\text{and}\space\vec{B}\text{are perpendicular to}\space\vec{c}$$ These three vectors form a right handed system, so that $$\vec{E}×\vec{B}\space\text{is along}\vec{c}$$, they are mutually perpendicular to each other. For ordinary light, $$\vec{E} \text{and} \vec{B}\space\text{are in all directions in a plane perpendicular to the}\\\space\vec{c}\space\text{vector - unpolarised waves.}$$ $$\text{If}\space\vec{E}\space\text{and (hence} \vec{B}\space\text{also ) is confined to a single plane only} $$ $$(\perp \vec{c}, \text{we have linearly polarized light. The plane containing} \vec{E} (or \vec{B}) and\space\vec{c} remains fixed.\\\text{ Hence, a linearly polarised light is also called plane polarised light. Plane of polarisation (contains )} \vec{E} and \vec{c};$$ polarisation by reflection; Brewster’s law: tan i_p=n; refracted ray is perpendicular to reflected ray for i= i_p; i_p+r_p = 90° ; polaroids; use in the production and detection/analysis of polarised light, other uses. Law of Malus.

(a) Photo electric effect, quantization of radiation; Einstein's equation E_max = hυ - W₀; threshold frequency; work function; experimental facts of Hertz and Lenard and their conclusions; Einstein used Planck’s ideas and extended it to apply for radiation (light); photoelectric effect can be explained only assuming quantum (particle) nature of radiation. Determination of Planck’s constant (from the graph of stopping potential Vs versus frequency f of the incident light). Momentum of photon p=E/c=hν/c=h/λ.

(b) De Broglie hypothesis, phenomenon of electron diffraction (qualitative only). Wave nature of radiation is exhibited in interference, diffraction and polarisation; particle nature is exhibited in photoelectric effect. Dual nature of matter: particle nature common in that it possesses momentum p and kinetic energy KE. The wave nature of matter was proposed by Louis de Broglie, λ=h/p= h/mv. Davisson and Germer experiment; qualitative description of the experiment and conclusion.

(c) A simple modern X-ray tube (Coolidge tube) – main parts: hot cathode, heavy element anode (target) kept cool, all enclosed in a vacuum tube; elementary theory of X-ray production; effect of increasing filament current- temperature increases rate of emission of electrons (from the cathode), rate of production of X rays and hence, intensity of X rays increases (not its frequency); increase in anode potential increases energy of each electron, each X-ray photon and hence, X-ray frequency (E=hν); maximum frequency hν_max =eV; continuous spectrum of X rays has minimum wavelength λ_min= c/ν_max=hc/eV. Moseley’s law. Characteristic and continuous X rays, their origin. (This topic is not to be evaluated)

(ii) Nuclei

Composition and size of nucleus. Radioactivity, alpha, beta and gamma particles/rays and their properties; radioactive decay law. Mass-energy relation, mass defect; binding energy per nucleon and its variation with mass number; Nuclear reactions, nuclear fission and nuclear fusion. 

(a) Atomic masses and nuclear density; Isotopes, Isobars and Isotones – definitions with examples of each. Unified atomic mass unit, symbol u, 1u=1/12 of the mass of ¹²C atom = 1.66x10^-27kg). Composition of nucleus; mass defect and binding energy, BE= (∆m) c² . Graph of BE/nucleon versus mass number A, special features - less BE/nucleon for light as well as heavy elements. Middle order more stable [see fission and fusion] Einstein’s equation E=mc² . Calculations related to this equation; mass defect/binding energy, mutual annihilation and pair production as examples. 

(b) Radioactivity: discovery; spontaneous disintegration of an atomic nucleus with the emission of α or β particles and γ radiation, unaffected by physical and chemical changes. Radioactive decay law; derivation of N = Noe^-λt ; half-life period T; graph of N versus t, with T marked on the X axis. Relation between half-life (T) and disintegration constant (λ); mean life (τ) and its relation with λ. Value of T of some common radioactive elements. Examples of a few nuclear reactions with conservation of mass number and charge, concept of a neutrino.

Changes taking place within the nucleus included. [Mathematical theory of α and β decay not included]. 

(c) Nuclear Energy Theoretical (qualitative) prediction of exothermic (with release of energy) nuclear reaction, in fusing together two light nuclei to form a heavier nucleus and in splitting heavy nucleus to form middle order (lower mass number) nuclei, is evident from the shape of BE per nucleon versus mass number graph. Also calculate the disintegration energy Q for a heavy nucleus (A=240) with BE/A ∼ 7.6 MeV per nucleon split into two equal halves with A=120 each and BE/A ∼ 8.5 MeV/nucleon; Q ∼ 200 MeV. Nuclear fission: Any one equation of fission reaction. Chain reactioncontrolled and uncontrolled; nuclear reactor and nuclear bomb. Main parts of a nuclear reactor including their functions - fuel elements, moderator, control rods, coolant, casing; criticality; utilization of energy output - all qualitative only. Fusion, simple example of 4 $$^{1}H\xrightarrow{}^{4}\text{He}$$ and its nuclear reaction equation; requires very high temperature ∼ 10⁶ degrees; difficult to achieve; hydrogen bomb; thermonuclear energy production in the sun and stars. [Details of chain reaction not required].