{"id":34913,"date":"2022-11-21T12:43:28","date_gmt":"2022-11-21T07:13:28","guid":{"rendered":"https:\/\/tsboardsolutions.com\/?p=34913"},"modified":"2022-11-23T16:18:52","modified_gmt":"2022-11-23T10:48:52","slug":"ts-inter-2nd-year-physics-notes-chapter-13","status":"publish","type":"post","link":"https:\/\/tsboardsolutions.com\/ts-inter-2nd-year-physics-notes-chapter-13\/","title":{"rendered":"TS Inter 2nd Year Physics Notes Chapter 13 Atoms"},"content":{"rendered":"<p>Here students can locate <a href=\"https:\/\/tsboardsolutions.com\/ts-inter-2nd-year-physics-notes\/\">TS Inter 2nd Year Physics Notes<\/a> 13th Lesson Atoms to prepare for their exam.<\/p>\n<h2>TS Inter 2nd Year Physics Notes 13th Lesson Atoms<\/h2>\n<p>\u2192 J.J. Thomson thought that the positive charge of the atom is uniformly distributed through out the volume of the atom and the negatively charged electrons are embedded in it like seeds in a watermelon.<\/p>\n<p>\u2192 According to Rutherford the entire positive charge and most of the mass of the atom is concentrated in a small volume called nucleus. Electrons are revolving around the nucleus at some distance just as planets revolve around the sun.<\/p>\n<p>\u2192 Alpha particle scattering experiments on gold foil showed that size of nucleus is about 10<sup>-14<\/sup> to 10<sup>-15<\/sup> m and size of atom is nearly 10<sup>-10<\/sup> m.<\/p>\n<p>\u2192 Most of the atom is empty space. The electrons would be moving in certain orbits with some distance from nucleus just like planets around the sun.<\/p>\n<p>\u2192 Alpha particle scattering experiment :<br \/>\nMagnitude of force between \u03b1 &#8211; particle and gold nuclie is F = \\(\\frac{1}{4 \\pi \\epsilon_o} \\frac{(2 \\mathrm{e})(\\mathrm{Ze})}{\\mathrm{r}^2}\\) Where &#8216;r&#8217; is the distance between \u03b1 &#8211; particle and nucleus.<br \/>\nThe magnitude and direction of force changes continuously as it approaches the nucleus.<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/tsboardsolutions.com\/wp-content\/uploads\/2022\/10\/TS-Board-Solutions.png\" alt=\"TS Inter 2nd Year Physics Notes Chapter 13 Atoms\" width=\"183\" height=\"15\" \/><\/p>\n<p>\u2192 Impact Parameter: It is the perpendicular distance of the initial velocity vector of a particle from centre of nucleus.<br \/>\nIn case of head on collision impact parameter is minimum and \u03b1 &#8211; particle rebounds back (\u03b8 = \u03c0). For a large impact parameter \u03b1 &#8211; particle goes undeviated. The chance of head on collision is very small. It in turn suggested that mass of atom is much concentrated in a small volume.<\/p>\n<p>\u2192 Bohr postulates : Bohr model of hydrogen atom consists of three main postulates.<\/p>\n<ul>\n<li>Electrons in an atom could revolve in certain permitted stable orbits. Electrons revolving in these stable orbits do not emit or radiate any energy.<\/li>\n<li>The stable orbits are those whose orbital angular momentum is an integral multiple of h\/ 2\u03c0.<br \/>\ni. e., L = nh \/ 2\u03c0 where n = 1, 2, 3, &#8230;&#8230;&#8230;&#8230;&#8230;&#8230; etc. (an integer.)<br \/>\nThese stable orbits are also called as non &#8211; radiating orbits.<\/li>\n<li>An electron may take a transition between non-radiating orbits. When electron transition takes place a photon of energy equals to the energy difference between initial and final states will be radiated.<br \/>\nE = hv = E<sub>i<\/sub>&#8211; E<sub>j<\/sub><\/li>\n<\/ul>\n<p>\u2192 Bohr radius (a<sub>0<\/sub>): According to Bohr theory radius of the orbit, r = \\(\\frac{\\mathrm{n}^2 \\mathrm{~h}^2 \\epsilon_0}{\\pi \\mathrm{me}^2}\\) when n = 1. It is called first orbit. Radius of 1st orbit r<sub>1<\/sub> = \\(\\frac{h^2 \\epsilon_0}{\\pi \\mathrm{me}^2}\\) = 5.29 \u00d7 10<sup>-11<\/sup> m. This is called Bohr orbit a<sub>0<\/sub>.<br \/>\na<sub>0<\/sub> = \\(\\frac{h^2 \\epsilon_0}{\\pi \\mathrm{me}^2}\\) = 5.29 \u00d7 10<sup>-11<\/sup> m = 0.529 \u00c5<\/p>\n<p>\u2192 Energy of orbit: From Bohr theory energy of the orbit E = &#8211;\\(\\frac{m e^4}{8 n^2 h^2 \\epsilon_o^2}\\)<br \/>\nWhere &#8211; ve sign indicates the force of attraction between electron and nucleus.<br \/>\nFor 1st orbit n = 1.<br \/>\nIts energy E<sub>1<\/sub> = -2.18 \u00d7 10<sup>-18<\/sup> J or<br \/>\nE<sub>1<\/sub> = &#8211; 13.6 eV.<br \/>\nFor all other orbits their energy E = \\(\\frac{13.6}{n^2}\\) eV<br \/>\nNote: The energy of an atom is least (i.e., it has maximum &#8211; ve value) when electron is revolving with n = 1 orbit. This energy state (n = 1) is called lowest state of the atom or ground state. For ground state of hydrogen atom E = &#8211; 13.6 eV.<\/p>\n<p>\u2192 Spectral series: From Bohr model electrons are permitted to transit between the energy levels while doing so they will absorb or release the exact amount of energy difference of the initial and final states.<br \/>\n\u2234 Energy absorbed or released E = hv = E<sub>i<\/sub> &#8211; E<sub>f<\/sub><br \/>\nE = hv = \\(\\frac{\\mathrm{hc}}{\\lambda}=\\frac{m \\mathrm{e}^4}{8 \\varepsilon_{\\mathrm{o}} \\mathrm{h}^2}\\left[\\frac{1}{\\mathrm{n}_{\\mathrm{i}}^2}-\\frac{1}{\\mathrm{n}_{\\mathrm{f}}^2}\\right]\\) or<br \/>\n\\(\\frac{1}{\\lambda}=\\mathrm{R}\\left[\\frac{1}{\\mathrm{n}_{\\mathrm{i}}^2}-\\frac{1}{\\mathrm{n}_{\\mathrm{f}}^2}\\right]\\) where R is Rydberg&#8217;s constant R = 1.03 \u00d7 10<sup>7<\/sup> \/ m<\/p>\n<p>\u2192 Lyman series: When electrons are jumping on to the first orbit from higher energy levels then that series of spectral lines emitted are called \u201dlyman series&#8221;.<br \/>\nIn Lyman series \\(\\frac{1}{\\lambda}=\\mathrm{R}\\left[\\frac{1}{1^2}-\\frac{1}{n^2}\\right]\\) where n = 2, 3, &#8230;&#8230; etc<\/p>\n<p>\u2192 Balmer series : When electrons are jumping on to the second orbit from higher levels then that series of spectral lines are called &#8220;Balmer series&#8221;.<br \/>\nFor Balmer series \\(\\frac{1}{\\lambda}=\\mathrm{R}\\left[\\frac{1}{2^2}-\\frac{1}{\\mathrm{n}^2}\\right]\\) where n = 3,4,&#8230;&#8230;&#8230;. Spectral lines of Balmer series are in visible region.<\/p>\n<p>\u2192 Paschen series : When electrons are jump\u00acing on to the 3rd orbit from higher energy levels then that series of spectral lines are called &#8220;Paschen series&#8221;.<br \/>\nFor Paschen series \\(\\frac{1}{\\lambda}=\\mathrm{R}\\left[\\frac{1}{3^2}-\\frac{1}{\\mathrm{n}^2}\\right]\\)<br \/>\nn = 4, 5&#8230;&#8230;&#8230;&#8230;.. These spectral lines are in near infrared region.<\/p>\n<p>\u2192 Brackett series: When electrons are jump\u00acing on to the 4th orbit from higher levels then that series of spectral lines are called &#8220;Brackett series&#8221;.<br \/>\nFor Brackett series \\(\\frac{1}{\\lambda}=\\mathrm{R}\\left[\\frac{1}{4^2}-\\frac{1}{n^2}\\right]\\) where n = 5, 6, &#8230;&#8230;&#8230;&#8230;&#8230;.<br \/>\nBrackett series are in middle infrared region.<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/tsboardsolutions.com\/wp-content\/uploads\/2022\/10\/TS-Board-Solutions.png\" alt=\"TS Inter 2nd Year Physics Notes Chapter 13 Atoms\" width=\"183\" height=\"15\" \/><\/p>\n<p>\u2192 Pfund series: When electrons are jumping on to the 5th orbit from higher energy levels then that series of spectral lines are called<br \/>\n&#8220;pfund series&#8221;.<br \/>\nFor pfund series \\(\\frac{1}{\\lambda}=\\mathrm{R}\\left[\\frac{1}{5^2}-\\frac{1}{\\mathrm{n}^2}\\right]\\)<br \/>\nwhere n = 6, 7, &#8230;&#8230;&#8230;&#8230; These spectral lines are in far infrared region.<\/p>\n<p>Note : In spectral lines \\(\\frac{1}{\\lambda}=\\mathrm{R}\\left[\\frac{1}{\\mathrm{n}_{\\mathrm{i}}^2}-\\frac{1}{\\mathrm{n}_{\\mathrm{f}}^2}\\right]\\)R<br \/>\nBut \\(\\frac{1}{\\lambda}\\) = v\/c<\/p>\n<p>Frequency of spectral line v = Rc\\(\\left[\\frac{1}{n_i^2}-\\frac{1}{n_f^2}\\right]\\)<\/p>\n<p>\u2192 Ionisation potential : It is the amount of minimum energy required to release an ele-ctron from the outer most orbit of the nucleus.<br \/>\nFrom Bohr&#8217;s model energy of the orbit is the ionisation energy of electron in that orbit.<br \/>\nEx: Energy of 1st orbit in hydrogen is 13.6 eV.<br \/>\nPractically ionisation potential of hydro-gen is 13.6 eV.<br \/>\nNote : The success of Bohr atom model is in the prediction of ionisation energy of orbits.<\/p>\n<p>\u2192 Force between &#8216;a&#8217; particle and positively charged nucleus<br \/>\nF = \\(\\frac{1}{4 \\pi \\varepsilon_o} \\frac{2 \\mathrm{e}(\\mathrm{Ze})}{\\mathrm{r} 2}=\\frac{\\mathrm{Ze}^2}{2 \\pi \\varepsilon_0 r^2}\\)<\/p>\n<p>\u2192 Kinetic energy of \u03b1 &#8211; particle,<br \/>\nK = \\(\\frac{2 Z \\mathrm{e}^2}{4 \\pi \\varepsilon_{\\mathrm{o}} \\mathrm{d}}=\\frac{Z \\mathrm{e}^2}{2 \\pi \\varepsilon_{\\mathrm{o}} \\mathrm{d}}\\)<\/p>\n<p>\u2192 Distance of closest approach d = \\(\\frac{\\mathrm{Ze}^2}{2 \\pi \\varepsilon_0 \\mathrm{k}}\\)<\/p>\n<p>\u2192 For an electron moving in the orbit of hydrogen atom = \\(\\frac{m v^2}{r}=\\frac{1}{4 \\pi \\varepsilon_o} \\frac{Z^2}{r^2}\\)<\/p>\n<p>\u2192 For an atom of atomic number \u2018Z\u2019, \\(\\frac{\\mathrm{mv}^2}{\\mathrm{r}}=\\frac{1}{4 \\pi \\varepsilon_{\\mathrm{o}}} \\frac{\\mathrm{Ze}^2}{\\mathrm{r}^2}\\)<\/p>\n<p>\u2192 Relation between orbit radius and velocity in hydrogen atom is r = e<sup>2<\/sup> \/ 4\u03c0\u03b5<sub>0<\/sub><br \/>\nmv<sup>2<\/sup> = \\(\\frac{1}{4 \\pi \\varepsilon_o}\\) where k = \\(\\frac{1}{4 \\pi \\varepsilon_o}\\) = 9 \u00d7 10<sup>9<\/sup><\/p>\n<p>\u2192 In hydrogen atom .<br \/>\n(1) Kinetic energy K = \\(\\frac{1}{2}\\)mv<sup>2<\/sup><\/p>\n<p>(ii) Potential energy U = \\(\\frac{\\mathrm{e}^2}{8 \\pi \\varepsilon_o \\mathrm{r}}=\\frac{m \\mathrm{e}^4}{8 \\mathrm{n}^2 \\mathrm{~h}^2 \\varepsilon_o^2}\\)<br \/>\n= \\(-\\frac{e^2}{4 \\pi \\varepsilon_o r}\\) (-ve sigh for force of attraction)<\/p>\n<p>(iii) Total energy E = K + U<br \/>\n= \\(-\\frac{e^2}{8 \\pi \\varepsilon_o r}=\\frac{-m e^4}{8 n^2 h^2 \\varepsilon_o^2}\\)<\/p>\n<p>(iv) Velocity of electron in orbit v = e\/\\(\\sqrt{4 \\pi \\varepsilon_o \\mathrm{mr}}\\)<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/tsboardsolutions.com\/wp-content\/uploads\/2022\/10\/TS-Board-Solutions.png\" alt=\"TS Inter 2nd Year Physics Notes Chapter 13 Atoms\" width=\"183\" height=\"15\" \/><\/p>\n<p>\u2192 Spectral series: Wavelengths of spectral series are given by \\(\\frac{1}{\\lambda}=\\mathrm{R}\\left(\\frac{1}{\\mathrm{n}_1^2}-\\frac{1}{\\mathrm{n}_2^2}\\right)\\)<br \/>\nwhere n<sub>1<\/sub> and n<sub>2<\/sub> are the number of orbits between which electron transition takes place.<br \/>\nEnergy radiated In transition E = hv = E<sub>2<\/sub> &#8211; E<sub>1<\/sub><br \/>\nIn Bohr atom model.<br \/>\nAngular momentum of orbital L = mvr = \\(\\frac{\\mathrm{nh}}{2 \\pi}\\)<br \/>\nradius of nth orbit r<sub>n<\/sub> = \\(\\frac{\\mathrm{nh}}{2 \\pi}\\)<\/p>\n<p>Velocity of electron in nth orbit<br \/>\nV<sub>n<\/sub> = e\/\\(\\sqrt{4 \\pi \\varepsilon_o m r_n}\\)<br \/>\nor v<sub>n<\/sub> = \\(\\frac{1}{\\mathrm{n}} \\frac{\\mathrm{e}^2}{4 \\pi \\varepsilon_{\\mathrm{o}}} \\frac{1}{(\\mathrm{~h} \/ 2 \\pi)}\\)<br \/>\nor<br \/>\nr<sub>n<\/sub> = \\(\\frac{\\mathrm{n}^2 \\mathrm{~h}^2 \\varepsilon_0}{\\pi \\mathrm{me}^4}\\)<br \/>\nBohr radius a<sub>0<\/sub> = \\(\\frac{h^2 \\varepsilon_o}{\\pi m e^4}\\) = 5.29 \u00d7 10<sup>-11<\/sup> m<\/p>\n<p>Energy of nth orbit<br \/>\nE<sub>n<\/sub> = \\(\\frac{-\\mathrm{me}^4}{8 \\mathrm{n}^2 \\mathrm{~h}^2 \\varepsilon_{\\mathrm{o}}^2}=\\frac{-2.18 \\times 10^{-18}}{\\mathrm{n}^2}\\)J = \\(\\frac{-13.6}{n^2}\\)eV<br \/>\nRydberg&#8217;s constant R = \\(\\frac{m \\mathrm{e}^4}{8 \\varepsilon_o^2 h^3 \\mathrm{c}}\\)<br \/>\n= 1.03 \u00d7 10<sup>7<\/sup> m<sup>-1<\/sup><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here students can locate TS Inter 2nd Year Physics Notes 13th Lesson Atoms to prepare for their exam. TS Inter 2nd Year Physics Notes 13th Lesson Atoms \u2192 J.J. Thomson thought that the positive charge of the atom is uniformly distributed through out the volume of the atom and the negatively charged electrons are embedded &#8230; <a title=\"TS Inter 2nd Year Physics Notes Chapter 13 Atoms\" class=\"read-more\" href=\"https:\/\/tsboardsolutions.com\/ts-inter-2nd-year-physics-notes-chapter-13\/\" aria-label=\"More on TS Inter 2nd Year Physics Notes Chapter 13 Atoms\">Read more<\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[26],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v19.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>TS Inter 2nd Year Physics Notes Chapter 13 Atoms - TS Board Solutions<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/tsboardsolutions.com\/ts-inter-2nd-year-physics-notes-chapter-13\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"TS Inter 2nd Year Physics Notes Chapter 13 Atoms - TS Board Solutions\" \/>\n<meta property=\"og:description\" content=\"Here students can locate TS Inter 2nd Year Physics Notes 13th Lesson Atoms to prepare for their exam. 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TS Inter 2nd Year Physics Notes 13th Lesson Atoms \u2192 J.J. Thomson thought that the positive charge of the atom is uniformly distributed through out the volume of the atom and the negatively charged electrons are embedded ... 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