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Covers full syllabus of Chapter 12 of NCERT class 12

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- 1. Ernest Rutherford Lect. Lovedeep Singh
- 2. INTRODUCTION The structure of matter that shapes the world around us has been a subject of study since long time. The first contribution in this regard came from Dalton who postulated that matter is made of atoms, which are indidvisible. The word atom comes from a Greek word Atomos which means ‘no cut’. J.J. Thomson proposed a sturcture for the atom, which was modified by Rutherford and later by Neils Bohr.
- 3. Dalton’s Atomic Theory All elements are consists of very small invisible particles, called atoms. Atoms of same element are exactly same and atoms of different element are different. Thomson’s Atomic Model Every atom is uniformly positive charged sphere of radius of the order of 10-10 m, in which entire mass is uniformly distributed and negative charged electrons are embedded randomly. The atom as a whole is neutral. This was also known as plum-pudding model of an atom.
- 4. Limitations of Thomson’s Atomic Model 1. It could not explain the origin of spectral series of hydrogen and other atoms. 2. It could not explain large angle scattering of α – particles. Rutherford’s α – Ray Scattering Experiment An α – particle is helium nucleus containing 2 protons and 2 neutrons. Therefore , an alpha particle has 4 units of mass. This experiment was done by Rutherford and his collaborators , Geiger and Marsden and is shown in fig.
- 5. ZnS
- 6. Conclusion A typical graph of the total number of α-particles scattered at different angles, in a given interval of time, is shown in Fig. The dots in this figure represent the data points. Many of the α-particles pass through the foil. It means that they do not suffer any collisions. Only about 0.14% of the incident α-particles scatter by more than 1º; and about 1 in 8000 deflect by more than 90º.
- 7. Conclusion Rutherford argued that, to deflect the α-particle backwards, it must experience a large repulsive force. This force could be provided if the greater part of the mass of the atom and its positive charge were concentrated tightly at its centre. This led Rutherford to postulate that entire positive charge of the atom must be concentrated in a tiny central core of the atom. This tiny central core of each atom was called atomic nucleus.
- 9. Distance of Closest Approach Distance of closest approach is the minimum distance between α- particle and centre of nucleus just before it reflects back by 180o When the distance between α-particle and the nucleus is equal to the distance of the closest approach ( ), the α-particle comes to rest. At this point or distance, the kinetic energy of α-particle is completely converted into electric potential energy of the system. Obviously, the radius of nucleus must be smaller than above value.
- 10. Impact Parameter The trajectory traced by an α-particle depends on the impact parameter, b of collision. The impact parameter is the perpendicular distance of the initial velocity vector of the α-particle from the central line of the nucleus. For large impact parameters, force experienced by α-particle is weak as F varies inversely as square of distance and α-particle will deviate much smaller and vice-versa. Rutherford calculated-
- 11. Rutherford’s Model of an Atom An atom is composed of positively charged particles. Majority of the mass of an atom was concentrated in a very small region. This region of the atom was called as the nucleus of an atom. It was found out later that the very small and dense nucleus of an atom is composed of neutrons and protons. Atoms nucleus is surrounded by negatively charged particles called electrons. The electrons revolve around the nucleus in a fixed circular path at very high speed. These fixed circular paths were termed as “orbits.” An atom has no net charge or they are electrically neutral because electrons are negatively charged and the densely concentrated nucleus is positively charged. A strong electrostatic force of attractions holds together the nucleus and electrons. The size of the nucleus of an atom is very small in comparison to the total size of an atom.
- 12. Electron Orbits The electrostatic force of attraction, Fe between the revolving electrons and the nucleus provides the requisite centripetal force (Fc) to keep them in their orbits. Thus, for a dynamically stable orbit in a hydrogen atom, Fe = Fc For hydrogen atom, Z= 1 The total energy of the electron is negative. This implies the fact that the electron is bound to the nucleus.
- 13. ATOMIC SPECTRA When an atomic gas or vapour is excited at low pressure, usually by passing an electric current through it, the emitted radiation has a spectrum which contains certain specific wavelengths only. A spectrum of this kind is termed as line emission spectrum and it consists of bright lines on a dark background. When white light passes through a gas and we analyze the transmitted light using a spectrometer we find some dark lines in the spectrum. These dark lines correspond precisely to those wavelengths which were found in the emission line spectrum of the gas. This is called the absorption spectrum of the material of the gas.
- 14. Spectral Series of Hydrogen Hydrogen is the simplest atom and therefore, has the simplest spectrum. In the observed spectrum, however, at first sight, there does not seem to be any resemblance of order or regularity in spectral lines. Each of these sets is called a spectral series. In 1885, the first such series was observed by a Swedish, Johann Jakob Balmer (1825–1898) in the visible region of the hydrogen spectrum. This series is called Balmer series . The line with the longest wavelength, 656.3 nm in the red is called Hα; the next line with wavelength 486.1 nm in the bluegreen is called Hβ, the third line 434.1 nm in the violet is called Hγ; and so on. Balmer found a simple empirical formula for the observed wavelengths Where n= 3,4,5…… R is a constant called the Rydberg constant & R = 1.097 x 107 m-1
- 15. Other series of spectra for hydrogen were subsequently discovered. These are known, after their discoverers, as Lyman, Paschen, Brackett, and Pfund series. These are represented by the formulae: Lyman Series n=2,3,4….. (Ultraviolet Region) Paschen Series n=4,5,6…. (Infrared Region) Brackett Series n=5,6,7…. ( ,,,, ) Pfund Series ( ,,,, ) n=6,7,8….
- 16. Limitations of Rutherford Atomic Model • Can’t explain Stability of atom According to classical electromagnetic theory, an accelerating charged particle emits radiation in the form of electromagnetic waves. The energy of an accelerating electron should therefore, continuously decrease. The electron would spiral inward and eventually fall into the nucleus. Thus, such an atom can not be stable. • Can’t explain Line spectra of atom Further, according to the classical electromagnetic theory, the frequency of the electromagnetic waves emitted by the revolving electrons is equal to the frequency of revolution. As the electrons spiral inwards, their angular velocities and hence their frequencies would change continuously, and so will the frequency of the light emitted. Thus, they would emit a continuous spectrum, in contradiction to the line spectrum actually observed.
- 17. Bohr’s Model of an Atom Niels Bohr (1885 – 1962) made certain modifications in this model by adding the ideas of the newly developing quantum hypothesis. Postulates of Bohr’s model:- 1. Every atom consist of central core called nucleus, in which entire positive charge and almost entire mass of atom are concentrated. A suitable no. Of electrons revolve around the nucleus in circular orbits. The centripetal force for revolution is provided by electrostatic force of attraction between electron and the nucleus. 2. Electron revolves around the nucleus only in those orbits for which the angular momentum is some integral multiple of h/2π where h is the Planck’s constant. Thus the angular momentum (L) of the orbiting electron is quantised. i.e. L = nh/2π 3. An electron might make a transition from one of its specified non-radiating orbits to another of lower energy. 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 then given by • hν = Ei – Ef
- 18. Radii of Bohr’s stationary orbits This shows that r ∝ / Z i.e. radii of stationary orbits are in the ratio 12:22:32: and so on. Clearly, the stationary orbits are not equally spaced. Putting values of all constants, we get This is called The Bohr’s radius. Velocity of electron in Bohr’s stationary orbit This shows r ∝ 1/ n Therefore, orbital velocity of electron in outer orbits is smaller as compared to its value in the inner orbits. For hydrogen, Z=1 and for n=1, v= 2.2X106m/s
- 19. Frequency of electron in Bohr’s stationary orbit It is the no. of revolutions completed per second by the electron in a stationary orbit around nucleus and is given by i.e. ν ∝ 1/ n For first orbit of hydrogen atom, ν= 6.57X1015 rps. Total energy of electron in Bohr’s stationary orbit putting standard values, for hydrogen, For ground state E= -13.6 eV. Therefore, the minimum energy required to remove the electron from ground state of hydrogen atom is 13.6 eV. This is called ionisation energy of hydrogen atom.
- 20. Bohr’s Explanation of Spectral Series Acc. to 3rd postulate of Bohr’ theory, when an electron makes a transition form orbit of higher energy to lower energy orbit, a light photon is emitted. When an electron jumps to 1st orbit (n=1) from any other orbit (n=2,3,4,….), Lyman Series is obtained which lies in ultraviolet region. Similarly, When an electron jumps to 2nd orbit (n=2) from any other orbit (n=3,4,5,….), Balmer Series is obtained which lies in Visible region.
- 21. When an electron jumps to 3rd orbit (n=3) from any other orbit (n=4,5,6, ….), Paschen Series is obtained which lies in Infrared region. When an electron jumps to 4th orbit (n=4) and 5th orbit from any other orbit (n=5,6,7 ….) and (n=6,7,8, …) Brackett and Pfund Series are obtained respectively which also lies in Infrared region. and
- 22. ENERGY LEVEL DIAGRAM A diagram which represents the total energies of electron in different stationary orbits of an atom is called energy level diagram. An electron can have any total energy above E=0 eV. In such a case, the electron is free.
- 23. Excitation energy:- The minimum energy required to excite an atom in the ground state to one of the higher stationary states is called excitation energy. e.g. in case of hydrogen, to lift an electron from ground state (E= -13.6 eV) to first excited state (E= -3.4 eV), energy is E= -3.4-(-13.6)= 10.2 eV Excitation Potential:- The minimum potential which provides an electron energy sufficient to jump from ground state to one of the higher states is called excitation potential. excitation potential= = 10.2 V Ionisation Energy:- The minimum energy required to ionise an electron is called ionisation energy. Ionisation Potential:- The minimum potential which would provide an energy to just remove an electron from atom is called ionisation potential.
- 24. de Broglie’ View of Bohr’s 2nd postulate. It states that the angular momentum of the electron orbiting around the nucleus is quantized (that is, L = nh/2π; n = 1, 2, 3 …). Why should the angular momentum have only those values that are integral multiples of h/2π? The French physicist Louis de Broglie explained this puzzle in 1923, ten years after Bohr proposed his model. We know that when a string is plucked, a vast number of wavelengths are excited. However only those wavelengths survive which have nodes at the ends. It means that in a string, standing waves are formed when the total distance travelled by a wave down the string and back is one wavelength, two wavelengths, or any integral number of wavelengths. For an electron moving in nth circular orbit of radius rn , the total distance is the circumference of the orbit, 2πrn. 2π rn = nλ, n = 1, 2, 3... Now, λ = h/mvn , we have 2π rn = n h/mvn m vn rn = nh/2π i.e. L = nh/2π
- 25. Limitations of Bohr’s Model 1. The Bohr model is applicable to hydrogenic atoms. It cannot be extended even to mere two electron atoms such as helium. Difficulty lies in the fact that each electron interacts not only with the positively charged nucleus but also with all other electrons. 2. While the Bohr’s model correctly predicts the frequencies of the light emitted by hydrogenic atoms, the model is unable to explain the relative intensities of the frequencies in the spectrum
- 26. LASER LIGHT The acronym LASER stands for Light Amplification by Stimulated Emission of Radiation. Since its development in 1960, it has entered into all areas of science and technology. It has found applications in physics, chemistry, biology, medicine, surgery, engineering, etc. There are low power lasers, with a power of 0.5 mW, called pencil lasers, which serve as pointers. There are also lasers of different power, suitable for delicate surgery of eye or glands in the stomach. Finally, there are lasers which can cut or weld steel.