PhysicsKund Physics class 9 to 12 NCERT, JEE - NEET

ELECTRIC POTENTIAL AT ANY POINT DUE TO AN ELECTRIC DIPOLE :  Obtain expression for the electric potential at any point due to an electric dipole. Rewrite this expression if point of observation lies on the (i) axial line of the dipole and (ii) equatorial line of the dipole. Consider any point P at a distance r from the centre (O) of the electric dipole AB. Let OP make an angle $\theta$ with the dipole moment $\vec{p}$. Let $r_1$ and $r_2$ be the distances of point P from -q charge and +q charge of the dipole respectively. Step 1. Potential at point P due to -q charge is given by $V_1 = \frac{1}{4\pi\epsilon_0} \frac{(-q)}{r_1}$ Potential at point P due to +q charge is given by $V_2 = \frac{1}{4\pi\epsilon_0} \frac{q}{r_2}$ $\therefore$ Using principle of superposition, potential at point P due to the dipole is given by $V = V_1 + V_2$ or $V = -\frac{1}{4\pi\epsilon_0} \frac{q}{r_1} + \frac{1}{4\pi\epsilon_0} \frac{q}{r_2}$ $V= \frac{q}{4\pi\epsilon_0} \left[ \frac{1}{r_2} - \frac{1...

Notes : CBSE Class 12 Physics Chapter 8 Electromagnetic Waves - Physicskund 1. Basic idea of displacement current,  2. Electromagnetic waves, their characteristics, their transverse nature (qualitative idea only). 3. Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, X-rays,gamma rays) including elementary facts about their uses.

Polarisation of Light Notes Class 12 PDF | NCERT, Board, NEET & JEE Polarisation Polarisation is an important property of light that proves light is a transverse wave. It is possible only in transverse waves because their vibrations occur perpendicular to the direction of propagation. Definition: Polarisation is the phenomenon in which the vibrations of a transverse wave are restricted to one direction (or one plane) perpendicular to the direction of propagation. Important Points: Only transverse waves can be polarised. Longitudinal waves cannot be polarised. Polarisation proves the transverse nature of light. Transverse Wave A transverse wave is a wave in which the particles of the medium vibrate perpendicular to the direction of propagation. For a wave travelling along the x-axis , the particles may vibrate along the y-axis or z-axis . Remember: The direction of vibration is always perpendicular to the direction of propagation. y-Polarised Wa...

Interference of Light Interference of light is the phenomenon in which two or more coherent light waves superpose and redistribute light intensity in space, producing regions of maximum and minimum intensity. Principle of Superposition The phenomenon of interference is based on the Principle of Superposition, which states: When two or more light waves overlap at a point, the resultant displacement at that point is equal to the vector sum of the displacements produced by the individual waves. Conditions for Sustained Interference The sources must be coherent. The waves must have the same frequency or wavelength. The phase difference between the waves should remain constant. The amplitudes should be nearly equal for clear interference patterns. Types of Interference 1. Constructive Interference Constructive interference occurs when two waves meet in the same phase. The resultant amplitude becomes maximum, producing maximum intensity. Condition: $\Delta = n...

Rutherford's Atomic Model According to Rutherford's nuclear model, an atom consists of a tiny, dense, positively charged nucleus at its centre, around which electrons revolve in circular orbits. Salient Features An atom has a small, dense, positively charged nucleus. Almost the entire mass of the atom is concentrated in the nucleus. Electrons revolve around the nucleus in circular orbits. The electrostatic force of attraction between the nucleus and electrons provides the necessary centripetal force. Most of the space inside an atom is empty. Electron Orbits Let, e = charge on electron Ze = charge on nucleus m = mass of electron v = velocity of electron r = radius of orbit ε 0 = permittivity of free space 1. Electrostatic Force of Attraction The electrostatic force between the nucleus and electron is given by: F e = Ze² / (4πε 0 r²) 2. Centripetal Force The centripetal force required for circular motion is: F c ...

Definition of Nuclear Fission  Nuclear fission is the process in which a heavy nucleus splits into two or more lighter nuclei when bombarded by a neutron. A large amount of energy and neutrons are released during this process. Example of Nuclear Fission When a slow neutron strikes a Uranium-235 nucleus, it first forms an unstable Uranium-236 nucleus. This unstable nucleus then splits into two lighter nuclei. Nuclear Reaction $${}^{1}_{0}n + {}^{235}_{92}U \rightarrow {}^{236}_{92}U$$ $${}^{236}_{92}U \rightarrow {}^{144}_{56}Ba + {}^{89}_{36}Kr + 3\,{}^{1}_{0}n + \text{Energy}$$ Important Points About Nuclear Fission Uranium-235 is a fissile material. Nuclear fission is a neutron-induced reaction. Two or more lighter nuclei are formed. 2 to 4 neutrons are released. The fission fragments are radioactive. They emit beta particles and eventually become stable. Energy Released in Nuclear Fission The energy released during fission is called the Q-valu...

Notes : CBSE Class 12 Physics Chapter 13 Nuclei - Physics Kund Composition of the Nucleus of an Atom Atomic Mass Unit Proton: Definition, Discovery and Properties Neutron: Definition, Discovery and Properties Define Isotopes, Isobars and Isotones with Example Size of the Nucleus: Derivation of Radius and Nuclear Density Einstein Mass-Energy Relation Mass Defect and Nuclear Binding Energy Binding Energy per Nucleon and its Variation with Mass Number Nuclear Force Radioactivity Nuclear Fission Nuclear Fusion

Notes : Shell Theorem and Gravitation Shielding - FAQ and Quiz - Class 11 Physics   Shell Theorem The Shell Theorem describes the gravitational effect of a uniform hollow spherical shell on a point mass placed either outside or inside the shell. (i) Point Mass Outside a Uniform Spherical Shell Statement: The force of attraction between a hollow spherical shell of uniform density and a point mass situated outside it is just as if the entire mass of the shell were concentrated at the centre of the shell. The gravitational force is given by: \[ F=\frac{GMm}{r^2} \] where, G = Universal gravitational constant M = Mass of the shell m = Mass of the particle r = Distance of the particle from the centre of the shell (ii) Point Mass Inside a Uniform Spherical Shell Statement: The force of attraction due to a hollow spherical shell of uniform density on a point mass situated inside it is zero. \[ F = 0 \] Summary of Shell Theorem Inside th...

According to Bohr's theory, an electron in a hydrogen atom can occupy only certain discrete energy states. The energy of an electron in the n th orbit is given by: $$E_n=-\frac{13.6}{n^2}\;eV$$ where, E n = Energy of the electron in the n th orbit n = Principal quantum number (1, 2, 3, ...) 13.6 eV = Ionization energy of hydrogen atom in the ground state Energy of Different Orbits (i) When n = 1 ( K Shell ) : $$E_1=-\frac{13.6}{(1)^2}=-13.6\;eV$$ The electron revolves in the innermost orbit (K-shell). This is the lowest possible energy of the hydrogen atom. Therefore, the atom is said to be in its ground state . (ii) When n = 2 ( L Shell ) :  $$E_2=-\frac{13.6}{(2)^2}=-\frac{13.6}{4}=-3.4\;eV$$ This corresponds to the first excited state of the hydrogen atom. (iii) When n = 3 ( M Shell ) :  $$E_3=-\frac{13.6}{(3)^2}=-\frac{13.6}{9}=-1.51\;eV$$ This is the energy of the second excited state of the hydrogen atom. (iv) When n = 4 ( N Shell...

Bohr’s Theory of Hydrogen Atom :  Hydrogen atom consists of a nucleus having charge $+e$ and an electron having charge $-e$.  The electron is assumed to revolve around the nucleus in circular orbit of radius $r$. Speed of Electron in terms of radius of an orbit of Hydrogen atom Coulomb’s force of attraction between the nucleus and the electron revolving in an orbit of radius $r_n$ is given by $F_n = \frac{1}{4 \pi \epsilon_0} \cdot \frac{e \cdot e}{r_n^2} = \frac{e^2}{4 \pi \epsilon_0 r_n^2}.....(1)$ This force provides the necessary centripetal force for the electron to move in a circular orbit of radius $r_n$ with a speed $v_n$. $F_c=F_n$ $\frac{m v_n^2}{r_n} = \frac{e^2}{4 \pi \epsilon_0 r_n^2}$ $m v_n^2 = \frac{e^2}{4 \pi \epsilon_0 r_n}.......(2)$ According to Bohr’s postulate of quantization of angular momentum, $L_n = m v_n r_n = \frac{nh}{2\pi}$ $\therefore \quad v_n = \frac{nh}{2 \pi m r_n} ........(3)$ Radius of an orbit of Hydrogen atom On the basis of Bohr’s atomic...

According to Bohr's model, electrons in a hydrogen atom revolve only in certain permitted orbits having definite energies. When an electron transitions from a higher energy state to a lower energy state, the difference in energy is emitted as a photon. Since only specific energy levels are allowed, the emitted radiation consists of discrete frequencies, producing the line spectrum of hydrogen . Bohr's Third Postulate When an electron makes a transition from a higher energy level (ni) to a lower energy level (nf), where ni > nf, the energy difference is emitted as electromagnetic radiation. Formula: hν if = E ni − E nf where: h = Planck's constant ν if = frequency of emitted radiation E ni = energy of the initial state E nf = energy of the final state Since ni and nf are integers, only certain frequencies are emitted. Therefore, the hydrogen atom produces a line spectrum. Energy of the Electron in Hydrogen Atom The total energy o...

Alpha-Particle Trajectory and Impact Parameter Class 12 Physics | Chapter 12: Atoms 12.2.1 Alpha-Particle Trajectory The trajectory (path) of an alpha-particle depends upon the impact parameter (b) . Definition of Impact Parameter The impact parameter (b) is the perpendicular distance between the centre of the nucleus and the initial direction of motion (velocity vector) of the alpha-particle when it is far away from the nucleus. A beam of alpha-particles contains particles having different values of impact parameter. Therefore, they are scattered through different angles. However, all alpha-particles possess nearly the same kinetic energy . Effect of Impact Parameter on Scattering 1. Small Impact Parameter (Small b) The alpha-particle passes very close to the nucleus. Strong electrostatic repulsion acts between the positively charged nucleus and alpha-particle. The scattering angle ( θ ) becomes large. For a head-on collision, the alpha-particle...

The Rutherford, Geiger and Marsden Experiment , also known as the Alpha Particle Scattering Experiment or Gold Foil Experiment , was performed in 1911. This experiment led to the discovery of the atomic nucleus and the development of Rutherford's Nuclear Model of the Atom. Introduction Ernest Rutherford, along with Hans Geiger and Ernest Marsden, conducted experiments to study the scattering of alpha particles by thin gold foils. The results of these experiments completely changed the understanding of atomic structure. What is an Alpha Particle? An alpha particle is the nucleus of a helium atom. Charge on alpha particle = +2e Mass of alpha particle ≈ 4 times the mass of a proton Experimental Setup Radioactive Source: Bi-214 was used as the source of alpha particles. Lead Block with Collimator: It produced a narrow beam of alpha particles. Thin Gold Foil: A gold foil of thickness approximately 2.1 × 10 -7 m was used. ZnS Screen: A zinc sulphide coated sc...

Introduction Atoms are the basic building blocks of matter. An atom consists of three basic particles: electrons, protons, and neutrons . In 1808, John Dalton proposed a theory of the atom according to which atoms of a particular element are identical and could not be subdivided further. The discovery of the electron by J. J. Thomson led him to propose the structure of the atom. Thomson suggested that atoms contain negatively charged particles called electrons and also possess positive charge so that the overall atom remains electrically neutral. Thomson’s Atomic Model Main Postulates An atom contains negatively charged particles called electrons . Since an atom is electrically neutral, it must also contain positive charge . The positive charge is uniformly distributed throughout the atom. Electrons are embedded within this positively charged sphere. This model is known as the Plum Pudding Model . Structure of the Atom According to Thomson, an atom is a...