PhysicsKund Physics class 9 to 12 NCERT, JEE - NEET

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 ...

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...

Notes : CBSE Class 12 Physics Chapter 12 Atoms - Physics Kund J.J. Thomson's Model of Atom Rutherford, Geiger and Marsden Experiment (Alpha Particle Scattering Experiment) Alpha-Particle Trajectory and Impact Parameter Rutherford's Model of Atom – Electron Orbits | Limitations Bohr Model of Hydrogen Atom Expression for Radius of nth Possible Orbit, Velocity and Energy of Electron in nth Orbit Energy Level Diagram of Hydrogen Atom Hydrogen Line Spectra De Broglie's Explanation of Bohr's Second Postulate of Quantization of Angular Momentum Drawbacks or Limitations of Bohr's Atomic Model

Learn Bohr's Theory of Hydrogen Atom in a simple and exam-oriented way. This Class 12 Physics article covers the limitations of Rutherford's atomic model, Bohr's three postulates, stationary orbits, quantization of angular momentum, and the emission and absorption of radiation. The notes are based on NCERT Physics and include FAQs and an interactive MCQ quiz with answers to help students revise effectively for board examinations and competitive exams Why was Rutherford's Model Unsuccessful? 1. Stability of the Atom According to classical electromagnetic theory: An electron moving in a circular orbit is an accelerated charged particle. Accelerated charged particles continuously emit electromagnetic radiation. As the electron emits radiation, it loses energy. Consequently, the radius of its orbit decreases continuously. The electron should therefore spiral into the nucleus. If this happened, atoms would collapse and could not exist in stable form. However...

Bohr's contribution to Rutherford's model of atom :  Rutherford's model of atom failed to explain the stability of atom as well as spectrum of radiations emitted and absorbed by an atom. To explain the concept of stability and the spectrum of an atom, Niels Henrik David Bohr applied Planck’s quantum theory of radiation to Rutherford’s atomic model. He used classical as well as quantum concepts to form his theory. Postulates of Bohr’s Atom Model  Bohr made the following assumptions popularly known as Postulates of Bohr’s atom model while proposing a new model for the atom: Postulate 1. Rutherford’s model of an atom is acceptable to the extent that an atom has a small positively charged core called nucleus where whole mass and positive charge of the atom are supposed to be concentrated. Postulate 2.  Bohr’s quantization condition for angular momentum states that electrons can revolve only in those energy levels, in which its angular momentum is an integral multiple of $h/2\...

Derivation of Rydberg Formula for Hydrogen Atom Spectrum :  According to Bohr's model of the atom, energy is radiated in the form of a photon when an electron jumps from a higher energy state to a lower energy state. In other words, energy is radiated in the form of a photon when an electron jumps from an orbit of higher energy ($n_i$) to the lower energy orbit ($n_f$), where $n_i > n_f$. The energy of the emitted radiation or photon is given by: $h\nu = E_{ni} - E_{nf}$ Using  $E_n = \frac{-m e^4}{8 \varepsilon_0^2 h^2 n^2}$ we get $h\nu = \frac{-m e^4}{8 \varepsilon_0^2 h^2 n_i^2}- \left(\frac{-m e^4}{8 \varepsilon_0^2 h^2 n_f^2}\right)$ $h\nu = \frac{m e^4}{8 \varepsilon_0^2 h^2} \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right)$ $\nu = \frac{m e^4}{8 \varepsilon_0^2 h^3}\left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right)$ Using $c = \lambda \nu$, i.e. $\nu = \frac{c}{\lambda}$ in Eq. (2), we get $\frac{c}{\lambda} = \frac{m e^4}{8 \varepsilon_0^2 h^3}\left( \frac{1}{n_f^2} ...

Drawbacks or Limitations of Bohr's Atomic Model Question: What are the drawbacks of Bohr's model of atom? Solution:  Bohr's atomic theory lacks consistency and has its own contradictions. It is neither based on a pure quantum theory nor pure classical theory. Bohr's atomic model has the following limitations: 1. This model could not explain the spectra of complex atoms having more than one electron. But it successfully explains the spectra of simple atoms (i.e., the atoms having only one electron). For example, it can explain the spectra of hydrogen atom and hydrogen like atoms ($He^+, Li^{++}$ etc). 2. Bohr's model of atom could not explain fine structure of the spectral lines of Balmer series. When the spectral lines of a Balmer series was observed under a powerful microscope, it was found that each spectral line consists of closely spaced lines. 3. Bohr's atomic model does not give any indication regarding the arrangement and distribution of electrons in an a...

DE-BROGLIE'S EXPLANATION OF BOHR'S SECOND POSTULATE OF QUANTIZATION OF ANGULAR MOMENTUM (BOHR'S QUANTUM CONDITION FROM de-BROGLIE HYPOTHESIS) Bohr's quantum condition of angular momentum:  Bohr could not explain as to why only certain orbits or energy levels were allowed for orbiting the electrons around the nucleus of atom. However, de-Broglie established a connection between the wave nature of electron and the stable orbits in the Bohr's model of atom. de-Broglie assumed that an electron orbit would be stable only if it contained an integral multiple of electron wavelength. The first orbit must contain one electron wavelength, the second orbit must contain two electron wavelengths, the third orbit must contain three electron wavelengths and so on. Proof :  de-Broglie hypothesis is analogous to the standing waves formed on a vibrating string of certain length. He assumed the circumference of the orbit of an electron as the length of the string. Thus, the circumfere...

12.1 Choose the correct alternative from the clues given at the end of the each statement: (a) The size of the atom in Thomson’s model is .......... the atomic size in Rutherford’s model. (much greater than/no different from/much less than.) Solution: No different From  (b) In the ground state of ..........electrons are in stable equilibrium,while in .......... electrons always experience a net force.(Thomson’s model/ Rutherford’s model.) Solution: (i) Thomson's model ,(ii) Rutherford’s model (c) A classical atom based on .......... is doomed to collapse.(Thomson’s model/ Rutherford’s model.) Solution: Rutherford's model (d) An atom has a nearly continuous mass distribution in a ..........but has a highly non-uniform mass distribution in ..........(Thomson’s model/ Rutherford’s model.) Solution : Thomson's model, Rutherford's model (e) The positively charged part of the atom possesses most of the mass in .......... (Rutherford’s model/both the models.) Solution:   Bot...