{"id":135,"date":"2018-11-16T12:19:50","date_gmt":"2018-11-16T12:19:50","guid":{"rendered":"http:\/\/phyp06.epgpbooks.inflibnet.ac.in\/?post_type=chapter&p=135"},"modified":"2018-11-16T12:52:13","modified_gmt":"2018-11-16T12:52:13","slug":"spectral-classification-sahas-ionization-formula","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/chapter\/spectral-classification-sahas-ionization-formula\/","title":{"rendered":"Spectral Classification \u2013Saha\u2019s Ionization Formula"},"content":{"raw":"
\r\n\r\n \r\n\r\n1.\u00a0\u00a0<\/strong>Learning Outcomes<\/strong>\r\n\r\n \r\n\r\nAfter studying this module, you should be able to\r\n
    \r\n \t
  • understand that Saha\u2019s considered ionization process as akin to chemical reactions<\/li>\r\n \t
  • learn to derive Saha\u2019s ionization formula<\/span><\/li>\r\n \t
  • explain that the degree of ionization of a given species of atoms depends mainly on temperature<\/span><\/li>\r\n \t
  • appreciate that the electron pressure plays a crucial role in distinguishing stars within a spectral class<\/span><\/li>\r\n \t
  • derive the ratio of excited hydrogen atoms to the total number of hydrogen atoms<\/span><\/li>\r\n \t
  • explain why Balmer lines are strongest in spectral class A (<\/span>?<\/span>~ 10,000 K)<\/span><\/li>\r\n \t
  • compute the ratios of singly ionized helium and doubly ionized helium to the total\u00a0<\/span>number of helium atoms<\/li>\r\n \t
  • appreciate why helium lines of HeII are strong in spectral classes O and early B<\/span><\/li>\r\n \t
  • calculate the ratios of neutral, singly ionized and doubly ionized calcium atoms to the total number of calcium atoms<\/span><\/li>\r\n \t
  • appreciate the reason for CaII lines being intense in the temperature range 4,000 \u2013 7,500 K, and being present at a temperature as high as 14,000 K.<\/span><\/li>\r\n<\/ul>\r\n<\/div>\r\n
    \r\n\r\n \r\n\r\n \r\n\r\n2.\u00a0\u00a0<\/strong>Introduction<\/strong>\r\n\r\n \r\n

    In Module 12 we discussed the variety in stellar spectra. We found that the Harvard scheme of stellar classification cannot accommodate all this variety. Therefore, classes Q, P and Wolf- Rayet had to be introduced at the top of the classification and classes R and N were introduced at the bottom of the classification scheme. We also learnt of some of the prefixes and suffixes used along with the spectral class to fully describe the peculiarities of the stellar spectrum. As prelude to the derivation of Saha\u2019s ionization formula, we derived Boltzmann law governing the population of excited atomic states. We stopped short of deriving the Saha formula, which we take up in this module.<\/p>\r\n \r\n\r\n<\/div>\r\n

    \r\n\r\n\"\" \"\" \"\" \"\" \"\" \"\" \"\" \"\" \"\" \"\" \"\"\r\n\r\n<\/div>\r\n \r\n\r\nThe basic material is from Astronomy and Astrophysics with Elements of Cosmologyby V. B. Bhatia. It has been amplified with the help of the following sources:\r\n
      \r\n \t
    • https:\/\/en.wikipedia.org\/wiki\/Saha_ionization_equation<\/li>\r\n \t
    • http:\/\/www.physicallensonthecell.org\/chemical-potential<\/li>\r\n \t
    • http:\/\/www.phy.ohiou.edu\/~mboett\/astro401_fall12\/saha.pdf<\/li>\r\n \t
    • http:\/\/pms.iitk.ernet.in\/wiki\/index.php\/Derivation_of_Saha_Equation<\/li>\r\n \t
    • http:\/\/www2.astro.psu.edu\/users\/rbc\/a501\/saha.pdf<\/li>\r\n \t
    • https:\/\/www.mtholyoke.edu\/courses\/jlevine\/ast228\/HW\/boltzsahaprobs.pdf<\/li>\r\n \t
    • https:\/\/www.astro.umd.edu\/~miller\/teaching\/astr601\/lecture08.pdf<\/li>\r\n \t
    • https:\/\/www.tcd.ie\/Physics\/study\/current\/undergraduate\/lecture-notes\/py3a06\/PY3A06_Saha_equation_spectral_type_2011.pdf<\/li>\r\n \t
    • https:\/\/en.wikipedia.org\/wiki\/Meghnad_Saha<\/li>\r\n \t
    • http:\/\/www.iloveindia.com\/indian-heroes\/meghnad-saha.html<\/li>\r\n \t
    • http:\/\/www.vigyanprasar.gov.in\/scientists\/saha\/sahanew.htm<\/li>\r\n \t
    • http:\/\/www.saha.ac.in\/web\/founder\/founder-life-works?showall=1&limitstart=<\/li>\r\n \t
    • https:\/\/en.wikipedia.org\/wiki\/Tests_of_general_relativity<\/li>\r\n \t
    • http:\/\/www.insa.nic.in\/writereaddata\/UpLoadedFiles\/IJHS\/Vol34_1_5_RSingh.pdf<\/li>\r\n<\/ul>","rendered":"
      \n

       <\/p>\n

      1.\u00a0\u00a0<\/strong>Learning Outcomes<\/strong><\/p>\n

       <\/p>\n

      After studying this module, you should be able to<\/p>\n

        \n
      • understand that Saha\u2019s considered ionization process as akin to chemical reactions<\/li>\n
      • learn to derive Saha\u2019s ionization formula<\/span><\/li>\n
      • explain that the degree of ionization of a given species of atoms depends mainly on temperature<\/span><\/li>\n
      • appreciate that the electron pressure plays a crucial role in distinguishing stars within a spectral class<\/span><\/li>\n
      • derive the ratio of excited hydrogen atoms to the total number of hydrogen atoms<\/span><\/li>\n
      • explain why Balmer lines are strongest in spectral class A (<\/span>?<\/span>~ 10,000 K)<\/span><\/li>\n
      • compute the ratios of singly ionized helium and doubly ionized helium to the total\u00a0<\/span>number of helium atoms<\/li>\n
      • appreciate why helium lines of HeII are strong in spectral classes O and early B<\/span><\/li>\n
      • calculate the ratios of neutral, singly ionized and doubly ionized calcium atoms to the total number of calcium atoms<\/span><\/li>\n
      • appreciate the reason for CaII lines being intense in the temperature range 4,000 \u2013 7,500 K, and being present at a temperature as high as 14,000 K.<\/span><\/li>\n<\/ul>\n<\/div>\n
        \n

         <\/p>\n

         <\/p>\n

        2.\u00a0\u00a0<\/strong>Introduction<\/strong><\/p>\n

         <\/p>\n

        In Module 12 we discussed the variety in stellar spectra. We found that the Harvard scheme of stellar classification cannot accommodate all this variety. Therefore, classes Q, P and Wolf- Rayet had to be introduced at the top of the classification and classes R and N were introduced at the bottom of the classification scheme. We also learnt of some of the prefixes and suffixes used along with the spectral class to fully describe the peculiarities of the stellar spectrum. As prelude to the derivation of Saha\u2019s ionization formula, we derived Boltzmann law governing the population of excited atomic states. We stopped short of deriving the Saha formula, which we take up in this module.<\/p>\n

         <\/p>\n<\/div>\n

        \n

        \"\" \"\" \"\" \"\" \"\" \"\" \"\" \"\" \"\" \"\" \"\"<\/p>\n<\/div>\n

         <\/p>\n

        The basic material is from Astronomy and Astrophysics with Elements of Cosmologyby V. B. Bhatia. It has been amplified with the help of the following sources:<\/p>\n

          \n
        • https:\/\/en.wikipedia.org\/wiki\/Saha_ionization_equation<\/li>\n
        • http:\/\/www.physicallensonthecell.org\/chemical-potential<\/li>\n
        • http:\/\/www.phy.ohiou.edu\/~mboett\/astro401_fall12\/saha.pdf<\/li>\n
        • http:\/\/pms.iitk.ernet.in\/wiki\/index.php\/Derivation_of_Saha_Equation<\/li>\n
        • http:\/\/www2.astro.psu.edu\/users\/rbc\/a501\/saha.pdf<\/li>\n
        • https:\/\/www.mtholyoke.edu\/courses\/jlevine\/ast228\/HW\/boltzsahaprobs.pdf<\/li>\n
        • https:\/\/www.astro.umd.edu\/~miller\/teaching\/astr601\/lecture08.pdf<\/li>\n
        • https:\/\/www.tcd.ie\/Physics\/study\/current\/undergraduate\/lecture-notes\/py3a06\/PY3A06_Saha_equation_spectral_type_2011.pdf<\/li>\n
        • https:\/\/en.wikipedia.org\/wiki\/Meghnad_Saha<\/li>\n
        • http:\/\/www.iloveindia.com\/indian-heroes\/meghnad-saha.html<\/li>\n
        • http:\/\/www.vigyanprasar.gov.in\/scientists\/saha\/sahanew.htm<\/li>\n
        • http:\/\/www.saha.ac.in\/web\/founder\/founder-life-works?showall=1&limitstart=<\/li>\n
        • https:\/\/en.wikipedia.org\/wiki\/Tests_of_general_relativity<\/li>\n
        • http:\/\/www.insa.nic.in\/writereaddata\/UpLoadedFiles\/IJHS\/Vol34_1_5_RSingh.pdf<\/li>\n<\/ul>\n","protected":false},"author":4,"menu_order":8,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["prof-v-b-bhatia"],"pb_section_license":""},"chapter-type":[],"contributor":[58],"license":[],"class_list":["post-135","chapter","type-chapter","status-publish","hentry","contributor-prof-v-b-bhatia"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/chapters\/135","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/wp\/v2\/users\/4"}],"version-history":[{"count":4,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/chapters\/135\/revisions"}],"predecessor-version":[{"id":152,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/chapters\/135\/revisions\/152"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/chapters\/135\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/wp\/v2\/media?parent=135"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/pressbooks\/v2\/chapter-type?post=135"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/wp\/v2\/contributor?post=135"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/phyp06\/wp-json\/wp\/v2\/license?post=135"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}