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Atom Notes

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Published in: AIEEE | Physics
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Notes On Atom.  NCERT 12th class

Akhilesh K / Lucknow

4 years of teaching experience

Qualification: M.Sc (NIT Rourkela - 2019)

Teaches: All Subjects, English, Mathematics, Science, Chemistry, Physics, Algebra, IIT JEE Mains, AIPMT, NEET

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  1. Chapter 12 — ATOM — physics notes by Akhil INTRODUCTION The first model of atom was proposed by J.J. Thomson in 1898. According to this model, the positive charge of the atom is uniformly distributed throughout the volume of the atom and the negatively charged electrons are embedded in it like seeds in a watermelon. This model called plum pudding model of the atom. Planetary model of atom (also called nuclear model of the atom). Ernst Rutherford proposed a classic experiment of scattering of a-particles by atoms to investigate the atomic structure. According to this, entire positive charge and most of the mass of the atom is concentrated in a small volume called the nucleus with electrons revolving around the nucleus. ALPHA PARTICLE SCATTERING- Screen is made up of Zinc sulphide (ZnS). This experiment performs in vacuum chamber. They directed a beam of 5.5 Me V a-particles emitted from a Bi radioactive source at a thin metal foil of gold. Alpha-particles emitted by a Bi radioactive source were collimated into a narrow beam by their passage through lead bricks. The beam was allowed to fall on a thin gold foil of thickness 2.1 x 10-7 m. The scattered alpha-particles were observed through a rotatable detector consisting of Zinc sulphide screen and a microscope. The scattered a particles on striking the screen produced brief light flashes. These flashes may be viewed through a microscope. target Vacuum about m thick Lead bricks Beam of a-particles Source of cc-particles About 1 in 8000 is reflected back Observations : Some are deviated through a large angle B Most pass through ZnS Screen Detector (Microscope) 107 103 104 103 102 10 o 20 40 60 80 100 120 140 Scattering angle O (in degree) 160 180 (i) Most of the alpha particle pass straight through the gold foil or scattered with very small angle of deflections. Conclusion- an atom has a lot of empty space. (ii) A few a - particles scatter through large angles ( > 900).means whole of the positive charge was concentrated in a tiny region of atom, named as nucleus. (iii) Rarely, an a particle scattered through an angle of 1800. it must experience a large repulsive force from nucleus. size of the nucleus 10 15 m to 10 14 m. size of an atom was known to be 10 10 m. atom has large empty area. Magnitude of this repulsive force is F = , r is the distance between the a-particle 47TE0 r2 and the nucleus.
  2. Alpha-particle trajectory- trajectory traced by an a-particle depends on the impact parameter (b) of collision. Impact parameter is the perpendicular distance of the initial velocity vector of the a-particle from the centre of the nucleus. v/ a-particle close to the nucleus (small impact parameter) suffers large scattering. v/ impact parameter is minimum then a- particle rebounds back (0 T). v/ For large impact parameter, a-particle goes nearly undeviated or small deflection (0 0). Where 0 is angle of scattering. Electron orbits- b Target nucleus Electrostatic force of attraction, (F e) between the revolving electrons, nucleus provides centripetal force (Fc) to keep them in their orbits. For stable orbit in a hydrogen atom 1 (e) (e) mv2 4TtEO r2 2 v/ Relation between the orbit radius (r) and the electron velocity (v) is r — 4TtE0mv2 v/ kinetic energy (K) and electrostatic potential energy (U ) of the electron in hydrogen atom are 2 K = - mv 2 2 4TtEOr 2 87TE0r ( negative sign in U signifies that the electrostatic force is in the —r direction.) Total energy E of the electron in a hydrogen atom is 2 8Tte0r 2 e 2 4Tte0r 8TtEOr v/ Total energy of the electron is negative. This implies the fact that the electron is bound to the nucleus. v/ If E is positive, then an electron will not follow a closed orbit around the nucleus. ATOMIC SPECTRA- Spectrum of wavelengths of electromagnetic radiation emitted or absorbed during transitions of electrons between energy levels within an atom. Each element has a characteristic spectrum. It is of two types.
  3. Emission line spectrum- When atoms are excited they emit light of certain wavelength which correspond to different colors. The emitted light observed as a series of colored lines (bright lines) with dark background in between; this series of bright lines is called Emission line spectrum. Continuum White Prism Absorption spectrum- When white light passes through a gas and we analyse the transmitted light using a spectrometer we find some dark lines in the spectrum. These dark lines is called the absorption spectrum of material of the gas. Spectral series- Lyman series is in the ultraviolet, and the Paschen and Brackett series are in the infrared region. Hydrogen is the simplest atom and therefore, has the simplest spectrum. Balmer series lie in visible region of hydrogen spectrum. line with longest wavelength, 656.3 nm in red is called Ha. line with 486.1 nm in the blue green called Hß, third line 434.1 nm in the violet is called Hr. As the wavelength decreases, the lines appear closer together and are weaker in intensity. Balmer formula for the observed wavelengths 1 1 1 22 n 2 is the wavelength , R is Rydberg constant =1.097 x 107 m -1 and n have integral values 3, 4, 5.. Q- write Balmer formula in terms of frequency (v= 1 General formula 1 - RZ2(-!-; 4) ni Lyman series: 1 1 1 12 n 2 Paschen series: 1 1 1 32 n 2 Brackett series: 1 1 1 42 n2 Pfund series: 1 1 1 52 n2
  4. Limitation of Rutherford model- 1. 2. An object moves in a circle, then it has constant centripetal acceleration. According to classical electromagnetic theory, an accelerating charged particle emits radiation in the form of electromagnetic waves. Therefore, energy of an accelerating electron should continuously decrease. The electron would spiral inward and eventually fall into the nucleus. Thus, such an atom cannot be stable. 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 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. BOHR MODEL OF THE HYDROGEN ATOM- Bohr gives three postulates. Bohr's first postulate was that an electron in an atom could revolve in certain stable orbits without the emission of radiant energy, contrary to the predictions of electromagnetic theory. According to this postulate, each atom has certain definite stable states in which it can exist, and each possible state has definite total energy. These are called the stationary states of the atom. Bohr's second postulate defines these stable orbits. electron revolves around the nucleus only in those orbits for which the angular momentum is some integral multiple of — , where h is the Planck' s constant (= 6.626x10 34 Js). Thus the angular momentum (L) of the orbiting electron is quantized. L = 2m Bohr's third postulate, 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 hv=Ei Ef. where Ei and Efare the energies of the initial and final states and Ei > Ef nh L = mvr — 4Ttcomrn n 4Ttco (h/21t) Put value of mr= nh/2m7T, we get Now find value of rn=? For n=l ,orbit radius called bohr radius, ao h2Eo rue = 5.29x10 11 m h2so a 2 It me
  5. 2 8TtEOr Put value of rn in above equation, we get 2 n 1 1.6 x 10 19J, Energy of nth orbit in ev is given by 13.6 2 n negative sign of the total energy of an electron moving in an orbit means that the electron is bound with the nucleus. Energy levels- The energy of an atom is the least (largest negative value) when its electron is revolving in ground state ( n = 1). The lowest state of the atom, called the ground state, is that of the lowest energy, with the electron revolving in the orbit of smallest radius, called Bohr radius, ao . The energy of this state (n = 1) El = -13.6 ev. Minimum energy required to free the electron from the ground state of the hydrogen atom is 13.6 e V. It is called the ionization energy of the hydrogen atom. Atom may acquire sufficient energy to raise the electron to higher energy states called excited state. From these excited states the electron can then fall back to a state of lower energy, by emitting a photon in the process. Total energy. E o —0.85 1.51 —3.40 13.6 Unbound (ionised) a [orri = 3 Excited states Ground state Highest energy state corresponds to n = oo where energy is E = OeV. Then electron is free. This is the energy of the atom when the electron is completely removed (r ) from the nucleus and is at rest. LINE SPECTRA OF THE HYDROGEN ATOM- According to the third postulate of Bohr' s model, when an atom makes a transition from the higher energy state with quantum number ni to the lower energy state with quantum number nf (nf< ni), the difference of energy is carried away by a photon of frequency v such that Em-En
  6. me4 1 hv (f = 8c20h2 ni2 2 n Total enerO, E (eV) o Ionised atom series or v me4 1 8cäh3 ( n2 4 8c20h3c -0.85 -1.5 Paschen series 3.40 Balmer series by inserting all constant values we get R = 1.03 x 107m which is very close to (1-097 x 107 m-l) value obtained from Balmer formula. v/ This agreement between the theoretical and experimental values of the Rydberg constant provided confirmation of the Bohr' s model. Ground state 13.6 Lyman series When electrons jump from higher energy state to a lower energy state and photons are emitted. These spectral lines are called emission lines. when an atom absorbs a photon that has precisely the same energy needed by the electron in a lower energy state to make transitions to a higher energy state, the process is called absorption. DE BROGLIE'S EXPLANATION OF BOHR'S SECOND POSTULATE OF QUANTISATION- It states that the angular momentum of the electron orbiting around the nucleus is quantized (that For an electron moving in nth circular orbit of radius rn, the total distance is the circumference of the orbit, = 2nrn Electron has wave nature it proved by Davisson and Germer. So this circumference of standing waves is integral multiple of wavelength. Thus, 2Ttrn= 111, n = 1, 2, 3... h h 1 (p is momentum p mv' 2nrn = nh mvr = mv) Nucleus Hence proved Bohr's 2nd postulate of quantization.

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