{"id":80,"date":"2018-11-14T07:29:18","date_gmt":"2018-11-14T07:29:18","guid":{"rendered":"http:\/\/phyp10.epgpbooks.inflibnet.ac.in\/?post_type=chapter&p=80"},"modified":"2022-01-07T05:39:08","modified_gmt":"2022-01-07T05:39:08","slug":"spectra-of-alkali-metals","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/phyp10\/chapter\/spectra-of-alkali-metals\/","title":{"rendered":"Spectra of Alkali Metals"},"content":{"raw":"
\"epgp<\/a>\r\n<\/span><\/div>\r\n
\r\n\r\n \r\n\r\nContents:<\/strong>\r\n\r\n \r\n\r\n1.\u00a0\u00a0\u00a0\u00a0 Spectra of Alkali Atoms : Introduction\r\n\r\n2.\u00a0\u00a0\u00a0\u00a0 Spectrum of Na : Quantum Mechanical View\r\n\r\n3.\u00a0\u00a0\u00a0\u00a0 Screening Constant\r\n\r\n4.\u00a0\u00a0\u00a0\u00a0 Doublet Structure of Sodium Series Lines (Spin-Orbit interaction)\r\n\r\n5.\u00a0\u00a0\u00a0\u00a0 Spin- orbit interaction energy for non-penetrating orbits\r\n\r\n6.\u00a0\u00a0\u00a0\u00a0 Spin- orbit interaction energy for penetrating orbits\r\n\r\n7.\u00a0\u00a0\u00a0\u00a0 Spectral lines in emission spectra (Intensity rules) Summary\r\n\r\n \r\n

The students will be able to learn about spectra of alkali metals and spectra of sodium element and spin- orbit interaction energy of orbits.<\/p>\r\n \r\n

1. Spectra of Alkali Atoms : Introduction<\/strong><\/p>\r\n\r\n<\/div>\r\n

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The series of Alkali atoms contain Lithium (Z=3), Sodium(Z=11), Potassium(Z=19), Rubidium(Z=37) and Cesium(Z=55) and their configurations are 1s2<\/sup>2s,1s2<\/sup>2s2<\/sup>2p6<\/sup>3s,1s2<\/sup>2s2<\/sup>2p6<\/sup>3s2<\/sup>3p6<\/sup>4s, 1s2<\/sup>2s2<\/sup>2p6<\/sup>3s2<\/sup>3p6<\/sup>3d10<\/sup>4s2<\/sup>4p6<\/sup>5s, 1s2<\/sup>2s2<\/sup>2p6<\/sup>3s2<\/sup>3p6<\/sup>3d10<\/sup>4s2<\/sup>4p6<\/sup>4d10<\/sup>5s2<\/sup>5p6<\/sup>6s<\/p>\r\n \r\n

This suggest that an alkali atom consists of one or more closed shell of electron in its ground state and a single valance electron in a new shell in ns orbit.<\/p>\r\n \r\n

Now visualizing the two particle system with a lone (valance) electron subjected to Coulomb field of a point charge that is equivalent to proton of the diameter~ 10-15m and is thus the simplest spectra.<\/p>\r\n \r\n\r\nThe aim is to solve this two-body system exactly to find the wave functions and understand the meaning of the four quantum numbers \u00a0and \u00a0.\r\n\r\n \r\n\r\nKeeping in mind the shell model to understand the structure of the alkali spectra and It is the fact that the fine structure and magnetic field splitting are smaller than the gross structure energies by a factor of about\u00a0 \"\"\u00a0Fine structure and the field splitting of the transitions (lines) can be understood after the gross structure of the spectrum.\r\n\r\n \r\n\r\nSo far, on the basis of shell model, the atomic states are known.\r\n\r\n\"\"\r\n

OR valence electron of sodium is moving in a net field of \u00a0charge (due to the core of finite size) apparently like a lone (valence) electron in hydrogen atom, moves around the proton (point charge). Therefore it is assumed that the spectra of sodium atom are expected to be analogous to that of the hydrogen as in both the\u00a0cases, respective valence electron moves in a net field of \u00a0but with the difference that the field is from the finite size core in former whereas from a point charge (proton) field in the later case.<\/span><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n\"\"\r\n\r\n \r\n\r\nThe closed shell has Zero Total angular momentum and Zero spin angular momentum and designated as 1<\/sup>S0\r\n\r\n \r\n\r\nThe valance electron can be excited to various s,p,d,f,\u2026. Orbits those results in doublet terms.\r\n\r\n \r\n\r\n2.\u00a0\u00a0\u00a0\u00a0 Spectrum of Na: Quantum Mechanical View<\/strong>\r\n\r\n \r\n

As the potential energy in hydrogen atom is spherically symmetric, that is, it depends only on the radial coordinate \u2018r\u2019, its solution, like for all spherically symmetric systems, may be expressed as<\/p>\r\n\"\"\r\n\r\n<\/div>\r\n\u00a0\"\"<\/em>\r\n

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The orbital angular momentum for a completely filled shell, according to Pauli\u2019s principle, is zero and therefore, their charge distribution is spherically symmetric. Accordingly, in the case of sodium atom (for that matter in case of all alkali atoms) charge distribution in\u00a0 n=1 & 2 shells (completely filled shells) is spherically symmetric and is known as the core of the atom. Valence electron 3s is, therefore, regarded as moving in a central force field (force that depends only on distance and is completely independent of the angular position) of the core.<\/p>\r\n \r\n

Therefore, quantum mechanically also spectrum of sodium is expected to be similar to that of the hydrogen atom.<\/p>\r\n \r\n\r\nExperimental Observations\r\n\r\n \r\n

The transition of the electron from one energy level to another is governed by the selection rules \u039bl=\u00b11<\/p>\r\n \r\n

Experimental findings reveal that emission spectra of the alkali atoms can be analyzed into four chief series with the peculiarities as given below.<\/p>\r\n \r\n

First series consists of doublets; separation (in cm-1<\/sup> ) between the doublet components remains constant (say delta vs<\/sub> ) as far as the series extends. Series is termed as Sharp series<\/p>\r\n \r\n

This arises due to transition from 2S states to lowest 2P state. The lines are observed in visible and infrared regions and are quite narrow.<\/span><\/p>\r\n \r\n

Second series consists of doublets; separation (in \u00a0cm-1<\/sup>) between the doublet components decreases rapidly as the series extends to higher members. Series is termed as <\/span>Principal series<\/strong>. This arises due to transition from 2P state to 2S state. The lines are intense and are observed in absorption spectrum as most of the atoms are in ground state. The lines of this series are in ultraviolet region except one in visible region.<\/span><\/p>\r\n \r\n

Third series initially consists of triplets (three components) followed by apparent\u00a0<\/span>doublets; separation (in\u00a0cm-1<\/sup> \u00a0) between the outer components remains constant\u00a0<\/span>(say delta vd<\/sub> ) as far as the series extends. Series is termed as <\/span>Diffuse series<\/strong>. This arises due to transition from 2D state to 2P state. The lines lie in the visible and infrared region. The lines of this series are diffused on one end or both the end of line.<\/span><\/p>\r\n \r\n

Fourth series, termed as <\/span>Fundamental series<\/strong>, lies in far infra red region and consists of very close lying doublets. This arises due to transition from 2Fstate to the lowest 2D state. The lines of this series are in visible and infrared regions.<\/span><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n \r\n\r\nRemarks:<\/strong>\r\n\r\n \r\n