Afoms s Chapter wi 1 SS ee « Bohr's Model of Hydrogen Atom srford's Modal Sea ‘+ Hydrogen Spectrum or Line Spectra of Hydrogen Atom jectron Orbits ciel of atom was proposed by J} Thomson in 1898 called plum pudding model of the atom. Later, worked on it and named this model as Rutherford’s planetary model of atom in 1911. In 1913, Niels ied on the model named as Bohr model of H-atom, porticles Scattering Experiment By Rutherford ment was suggested by Rutherford in 1911 as given in the figure below Radioactive soutce of a-particles Most particles Gold fol aes ey \_ straight ine (10 m thick) == ‘Ss a a) Jo ae AMY 20s. Lead cavity Colimator About one arpartcle in 8000. ~ Microscope cacpartcles is reflected back detector Experimental arrangement for Rutherford's theory criment, H.Geiger and E,Marsden took *{$Bi as a source for o-particles. A collimated beam of energy 5.5 MeVewas allowed to fall on 2.1 x 10~’m thick gold foil. The o-particles were observed a rotatable detector consisting of a zinc sulphide screen and microscope and it was found that c-particles d ed c-particles produced bright flashes or scintillations on the zinc sulphide screen. Now, these were counted at different angles from the direction of incident beam.Observations Rutherford made the fllowing observations fom his cxperiment that are given below 10) Mos of the acpariles passed chrough the gold Pa without any appreciable deflection Gi Ont tous 0.1495 af th cient particles seattered by mo ‘every 8000 ocparticles (Gi) About one o-partile in deflected by more than 90° “The tal number of arpartics (N) rough an angle () i as shown in th Figure scattered re below ameoenind "ere een oe scattered per unit afea inversely a8 perinsta dea poi porns 67 (iy) The number of particles ING) at scattering ange @ varies sin*0/2 (v= rea | () The force beew given by een ocparticles and nucleus is T Be) ine. ance between the a-particles wor the nucleus. This force is directed along the fine joining the a-parice and che nucleus. The mnagninude and direction of this free on Gr particle consinuously changes sit approaches the nucleus and recedes away from it Condesions (On the bass of his experiment, that Gi) Atom has alot of empey space and practically the fhe atom is confined Co an where, ris the dis Rutherford concluded mold a rons evolve round ar omits ae the page ar obi 3 the ene ey SOL Her, dence of ape, 4 = 44 10° cexemely small ental core ella ‘omic muber, Z=79.KE, =? Sue i ofthe order fom 10°! m ri a Sarming of panic ia al sce gle oy ag 1 the Coulomb’ law of electron ye centre vided by the Carita _ tae Tulion eos he ae a 00 cn te eas 1 cloqetlenieeyy tats thd Orparticle, change won mules, . ae on ye ep acioci0rPxPe10 a ectron and na co osest approach i ae cance of the velo “ive whole ofthe inal Kegel of Seteing ‘particle From the central ine ie 2 hve Pal creel Aley whch eae dined oe iter isthe angle feet ie a the «ano of the stem cng pth oud the maces seed angle of RRP, Te suns pa are angle of 90° is 100 per minute Aha at acto es Inge Part) apendar distance of he vac vec of ‘of e-pariles, when iis s scattered ata ‘particle from the central line ofthe nucleus of the saricle approaches dhe mde he tom is clled impact parameter. Mathematically its pac of repulsion 4 ome 2 ery ofp eo rosa Pte comeing ceetance rom the nde wie «ne i a pea ce cs canes Aaa Seen a soa = sere of closest approach ee ira partcle = Elecooeae aay and KE =kinetic energy of particle = 5 ae” —*¢ Inexeothad-on-calision the impact parm it Bee ae parce inands ck = ae, (charge cn oR nucleus is Ze, cee ora ge impact parameter, the partie goes neatly tndevinted and has 2 small deflection (@= 0") ‘The essential features of Rutherford the atom or planetary model ofthe (i) Bvery atom consis ofa cen atomic nucleus, in which the Charge and almost ent concentrated. (i) The sie of nuclesis of the which is very small as atom which is ofthe order 1 1 ol ea eeepc tg cnet a aan a cereal cha seep je Speen hgh a Pie ic miea ce we eh ee cad DANPLE 2. tn a head-on-colis cleus, he dosestdi vo) a a Trajectory of porte clove fo on tom ‘The a-particles which pass through the atom at a close distance from the nucleus suffer a large deflection. The @-particles which travel rowards the nucleus directly, slow down and ultimately comes to rest and then after being deflected through 180° retrace their path. Electron Orbits The Rutherford nuclear model of the atom atom as an electrically neutral sphere consisting of a very small, massive and positively charged nucleus at the centre surrounded by the revolving electrons in their respective dynamically stable orbits. The electrostatic force of attraction (F,) between the revolving electrons and the nucleus provides the requisite centripetal force (F,) to keep them in their orbits. Thus, for a dynamically stable orbit in a H-atom, jictures the => (-Z=q Thus, the relation between the orbit radius and the electron velocity is 2) Ame, mv? The kinetic energy (K') and electrostatic potential energy (U) of the electron in H-atom are z ee dips eel ie 2 81657) 7 and (che negative sign in U signifies that the electrostatic force is attractive in nature.) Thus, the total mechanical energy F of the electron in | H-atom is The total energy of the electron j implies the fact that the electron ig nucleus. If F is positive, then » then an el follow a closed otbit around leave the atom, oe EXAMPLE 3. It is found experi 136 eV is required to separa a proton and an electro velocity ofthe electron in a Haan Sol. Total energy of the electron in TE=~136 eV 2-13.64 =—2.2% 10-18 y ‘We now that, total energy, TE. =5.3x 107m + Velocity of the revolving Regarding Stability of Atom Electrons revolving around the nud acceleration. According to theory, the electrons must electromagnetic wave, Due to this continuous loss 0 the radii of their orbits should decreasing and ultimately the ele the nucleus. Thus, atom cann arate a ground, in. Compute the,ra ns ot ion of Line Spectrum decrease in radii of electron’s orbit, Ho continue evolution of electron will also change qven© {sical theory of electromagnetism, ing OE wave emitted by electron is equal ro revolution of electron aie tli jontinwous y of waves of all ig, electron will radiate E sult td spectrum of these waves will be 1, experimentally we observe ne spectrum of a particular frequency. 1 model was unable to explain line poo cies and fears. Bu on inulin gh, Rutherford poht’s Model of Hydrogen Atom smbined classical and early quantum concepts noms theory in the form of three postulates are as follows Bohr’s first postulate was that an electron in an ‘tom could revolve in certain stable orbits without ine emission of radiant energy, contrary to the predictions of electromagnetic theory. According to ‘iis postulate, each arom has certain definite stable ‘tates in which it can exist and each possible state nas definite total energy. These are called the stationary states of the atom. ji) Bohr’s second postulate states that the electron revolves around the nucleus only in those orbits for ‘which the angular momentum is some integral multiple of 4/27, where h is the Planck’s constant 63 x10™™ J-s). Thus, the angular momentum (L) of the orbiting electron is quantised, ole 2n As, angular momentum of electron = mor ice +. For any permitted (stationary) orbit ‘mor an where, = any positive integer 1, 2, 3, Ieis also called principal quantum number. (ii) Bohr’s third postulate states that an electron mi make a transition from one of its specified non-radiating orbits to another of lower energy. When ic does so, a photon is emitted having energy cequal to the energy difference between the initial and final states The frequency of the emitted photon is given by w= E,-Ey where, E, and Ey are the energies of the initial and final states and E, > Ey. Bohr’s Radius of Hydrogen Atom According to Niels Bohr (a Danish physicist) electron revolves around nucleus in stationary orbits. In these orbits electron does not radiate energy. The radius of mth orbit of the H-atom, z eh 1m, where, €5 = permittivity of vacuum b= planck’s constant m, = mass of electron and nis also known as principal quantum number for n= Land putting values of constants, we get 885 x 107 x 663 x 10 for 3 12 314 x91 x 107 x (16 x 10") 29 x 10" m= 053A This is called Bohr radius Since, -.r, = 053 x 2°A, the radius of the second orbit of H-atom will be (4 x 0.53) A and that of the third orbit (9 x 0.53) A. Note Velocity and Energyh of electron in stationary orbits of thydrogen atoms are given by é met See The re = Beane EXAMPLE 4. In Bohr’s model of H-atom, the radius of the first electron orbit is 0.53 A. What will be the radius of the third orbit and the first orbit of singly ionised helium atom? 243 Sol Radius of chen Rok osbhiie=s aa mmZe* 1 ‘Again, rad fade Zu ny hnzies For hydrogen, Z =1 and for helium, Z =2this state has lowest enc eee ae G2GeV: Therefore the miner 8 8 wae free the electron from the gr d wae cP und state of the H-atom tion energy of the H-atom, ‘Most of the H-atoms are in is13.6eV. ten cia ge A om tp by electron colsons) he atom may song ee condition, che arom is aid tebe cen From the excited state, the clectron can fall back to lower energy state by emiuing shoe aie energy difference of the energy states. Unbound (onsed) -085—= 154 3.49 Ground state nat 13. level diagram for hydrogen tom Accor ing to Bohs ‘the emivted lees th nt dg ited state, Set. 0 Wee r FRANPLEG, A Hom nial es pinon chet n= 4 level, Determine the war photon ‘ Sol. To find the wave aa the relation of energy of et = 3.108 iy ‘Waeengh of phen, 4 xin Yabo 97510 Thos the wavelengths ey isa x10" He aed tiydrogen Spectrom or Line Spectra of Hydrogen Atom Inner specu oo of dt ae dak ackground andi psalm Sslogen eso sperm Thre ee Fa nr? 2 n nucleus. Hydrogen Spectrum The radiation emi : f emitted by an electron when it j ae of hydrogen atom is called hydrogen spectrum or emission Dee ae rogen. :om Pattern Exercise A Objective Questions choice Questions ering oF particles, Rutherfordy ed that (aio and is posidve charge were av centre of atom vw of ator fy concentrated at Gente of positive charge of atom is concentrated at of acon is uniformly distibuted dhroughout consist of a postively charged nucleus iv om the following observation of | Marselen experiment ot piles do not pas stag dough the gold fol suny of c-partiles ate seattered through the tute angles 1 luge number of particles ate deflected by ange angles of the above jing the Bohr radius as dy * 68 pm, the radius of 11" ion in its ground state, on the basis of ohr's model, will be about (NCERIT Exemplar) Spm (b) 27pm (18pm — (d) 13 pm . The de-Broghie wavelength of an electron in first Bohr's orbit is \ cual to of circumference of obit 1 » ual o + of circumference of orbit qual o twice of circumference of orbit cual co the circumference of orbi 5. In the o-particle scattering experiment, the hape of the trajectory of the scattered v-particles depend upon (All India 2020) ») only on impact parameter ») only on the soutee oF o-particles ) Hoth impact parameter and source of o-particles 1) impact parameter and the screen material of the detector 6. ‘The radius of the innermost electron orbit of a hydrogen atom Is 6.3 410°" m, The radius of the = Borbit is (CRS 2025, SOP) (10110 mH) 159% 10°" ow (22 «10m AIT 10°" om 7, ‘The potential energy of an electron in the necond excited state in hydrogen ator is (a) = BAe (b) = 802 eV () “15 1eV (A) 64 4, Aproton and an alpha particle have the same kinetic energy. The ratio of de-Broghie wavelengths associated with the proton to that with the alpha particle ta (a) 1 (b)2 1 (@avh @> 9, The radius of the nth orbit in Bohr model of hydrogen atom is proportional to 1 (an? ws (On @, Assertion and Reason Directions (Q. Nos. 10-11) In the following questions, two statements are given- one labeled Assertion (A) and the other labelled Reason (R). Select the correct answer fo these questions from the codes (a), (b), (c) and (d) as given below (@) Both Assertion and Reason are true and Reason is the correct explanation of Assertion. (b) Both Assertion and Reason are true but Reason is noe the correct explanation of Assertion. (6) Assertion is true but Reason is false. (@) Assertion is false but Reason is true. 10, Assertion (A) Large angle of scattering of alpha particles led to the discovery of atomic nucleus. Reason (R) Entire positive charge of atom is concentrated in the central core. 11, Assertion (A) Atom as a whole is electrically neutral, Reason (R) Atom contains equal amount of positive and negative charges.<§ DUES ETS UCSTIONS v answer Type Questions (0 calculate the radius of the first orbit of H-atom, Lal ° i ajso, find out the ratio a ; i f c.-particles in Explain, why scattering of Se experiment is not affected by the Ru mass of the nucleons? F ut the wavelength of the electron orbiting ima d state of hydrogen atom. Le in the groun es au ong Answer Type Questions Ss the three wavelength 7. Fi tion between shi 4 find pee from the energy le diagram Mo shawn halaur “= CTTEY level . 0.85 then Calculate the wavelen, ine emitted, To which Serie Spectrum, does this wavele 23, Calculate the wavelength associated with a proton | nergy. How will the wav for an alpha particle hav 24. (i) (a) Differentiate betw approach and inn (b) Determine the dis approach when a kinetic energy 3. nucleus of Z =7! directions. Or post Te semeepocuuim, Uves UUs Wavelengin belong? (All India 2012) 23. Calculate the wavelength of de-Broglie waves associated with a proton having (=) eV 1.673 energy. How will the wavelength be affected for an alpha particle having the same energy? 24. (i) (a) Differentiate between distance of closest approach and impact parameter. (b) Determine the distance of closest approach when an alpha particle of kinetic energy 3.95 MeV approaches a nucleus of Z =79 stops and reverses its directions. Or (ii) (a) State three postulates of Bohr’s theory of hvdraaen atam