| geigereMarsden’s a-particle Scattering Experiment onthe suggestion of Rutherford, in 1911, his two associates, H. Geiger and E. Marsden, performed Ondaperiment by bombarding -particles (Helium nuclei Z = 2,4 = 4) on a gold foil observations: {) Most of the a-particles pass through the gold foil undeflected. ii) Avery small number of acparticles (1 in $000) suffered large angle deflection; some of them retraced their path or suffered 180° detection, Conclusion: {) Atom is hollow. (i) Entire positive charge and nearly whole mass of atom is concentrated in a small centre called nucleus of atom. (ii) Coulomb's law holds good for atomic distances. (jo) Negatively charged electrons are outside the nucleus. Impact Parameter: The perpendicular distance of initial \elocity vector of a-particle from Rutherford Scatering experiment the nucleus, when the particle is far away from the nucleus, is called the impact p of a-particle, b = 0. Angle of Seatering (4): The angle by which a-particle is deviated from its original direction is arameter. It is denoted by 6. For head on approach called angle of scattering eg F yadda at 9 ane, Ex 2 bilarge ‘where £ is the initial kinetic energy for head on approach of alpha particle. Impact parameter, b= 0.2. Distance of Closest Approach ; i heavy nucleus is a measure of the si “The smallest distance of approach of arparticle NEAT i Seo ey Distance of nearest approach » size of nucleus = ne, “7 vchere Eis Kinetic energy of incident a-partcle, z= atomic number, ¢ = electronic charge, 3. Rutherford’s Atom Model ‘Atom consists ofa central he CGrculating around the nucle oe Rutherford model could explain the neutrality ofan atom therstjonve sities and photoeler: ‘effect; but it could not explain the stability of an atom and the observed line spectrum ofan sist (atomic spectrum). 4. Bohr's Model Bohr modified Rutherford atom m: Postulates of Boht’s Theory (Stationary Circular Orbits: An atom consists of a central positively charged nucleus and negatively charged electrons revolve around the \y nucleus in certain orbits called stationary orbits. 1 “The electrostatic coulomb force between electrons and the nucleus 9g Ns provides the necessary centripetal force. 3 | mmo? __1_ (2016) avy nyeleus containing positive charge and negatively charged eect leus in circular orbits. ms ‘odel to explain the line spectrum of hydrogen. ane, 7? where Zs the atomic number, m is the mass of electrons, r = radius of orbit. i Quantuin Condition: The stationary orbits are those in which angular momentum of elecron isan integral multiple of 22,4 mor angi, e123. Integer nt called the prinépal quantum number. This equation is called Boht’s quantum ition. (iii) Transitions: The electron does not radi net nit alee Th eo cere viet azica humps oat oe moar ct to the other. The frequency of emitted or absorbed photon is given by hv = |B,-E/| This is called Bohr's frequency condition. Radius of Orbit and Energy of Electron in Orbit Condition of motion of electron in circular orbit is mo® __1_(Ze)(e) are, 8) Bohr's quantum condition is eat mr eR al) = = °° Dome Substituting this value of vin (j), we get‘The value of Rydberg constant is 1.097 x 107 m We have a -(vit) For hydrogen atom Z Equations (it!) and (vii) indicate that radii and energies of hydrogen like atoms (i.¢., atoms containing one electron only) are quantised.5. Energy Levels of Hydrogen Atom “The energy of electron in hydrogen atom (2 Rh _ 136 .y, = 1)isgiven (or series ofhydrogen spectrum) jy 13.6 eV whenn=1, 0 Ey F, = Sev =-34eV when n when» = 38eve-1 5leV whenn = 4, 188 ey = -0.85eV “Astw whenn=5, Ey=—"pg eV =-O54eV me? dng - 13.6 whenn=6, By=—gg eV = ~0.38eV when n = 7, net 13600 Fig. (a) Energy Level Diagram whenn = ©, I these energies are expressed by vertical ines on proper scale, the diagram obtained is called the energy level diagram, The energy level diagram of hydrogen atom is shown in fig. (a). Clearly the sere) ion between lines goes on decreasing rapidly with increase of m (it, order of orbit). The series of lines of H-spectrum are shown in fig. (0). If the total energy of electron is above zero, the electron is free and can have any energy: Thus there is a continuum of energy states above F = 0 eV. 6. Hydrogen Spectrum Hydrogen emission spectrum consists of 5 series. (i) Lyman series: This lies in ultraviolet region. (ii) Balmer series: This lies in the visible region. (iii) Paschen series: This lies in near infrared region. (jo) Brackett series: This lies in mid infrared region. («) Pfund series: This lies in far infrared region. Hydrogen absorption spectrum consists of only Lyman series. Explanation of Hydrogen Spectrum: -n, and nyare the quantum numbers of initial and final states and and E,are energies of electron in H-atom (2 =1) in inital and final states then we have 5, =~ and £, = ME 2 nf Energy of absorbed photon * ae AE=E, E,= Rhe nt nt Ifvis the frequency of emitted radiation, we have from Bohr’s fourth postulate E, elaaye mumber (i., reciprocal of wavelength) of the emitted radiation is given by wi the yel¥ lia v e=R-5 nen? - €. i ie relation explains successfully the origin of various lines in the spectrum of hydrogen atom. ‘The series of lines are obtained due to the transition of electron from various other orbits to a janer orbit. ‘Continuum oev << 0.280 . + Hl “0:38 ov +. [tt “ossev 1 1 T + Phund seves “Secev HY] Brstet sees 4stev | Paschen series : n=2 -3400v ast ~136 ev Fig, (b) Series of H-spectrumShort Answer Questions Each ofthe following questions are of $ marks. a the rel Q.1. (@ State Bohr postulate of hydrogen atom that gives the relationship 1 fey ‘emitted photon in a transition. | . atom. How many maximum, di) An electron jumps from fourth to first orbitin an 0 . «a ae mrp by te atom? To which series these lines correspond? “reset ‘Ans. (i) Bohr’s third postulate: It states that 2 ea = ae from on, 4 ecified non-radiating orbits to another of I / does a oi cavitted having energy equal to the energy difference between the initial ang tin : “The frequency of the emitted photon is given by ie hy = E,-Ey ; where E,and Bare the energies ofthe initial and final states and E, > E,, i) Electron jumps from fourth to first orbit in an atom ‘Maximum number of spectral lines can be 4) 4x3 _ ‘= gq 2 78 In diagram, possible way in which electron can jump (above). ned nat yan Series ‘The line responds to Lyman series (¢” jumps to 1* orbit), Balmer series (¢ jumps to orbit), Paschen series (e" jumps to 3™ orbit). Q.2. Calculate the de-Broglie wavelength associated with the electron revolving in the first exciti state of hydrogen atom. The ground state energy of the hydrogen atom is -13.6 eV. [CBSE 2020 5551), of the electron in the first excited Ey= Bpev= 34eV =-34% 16% Associated kinetic energy = - E, K=5.44 x 10] + de-Broglie wavelength, 2 = hip he v2mK 6.63 x10" ian (99.008) x10-% = 0.663 x 10 m = 0.663 nm = 6.63