P31318Notes02[368].pdf - 11 The term value T is the energy...

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11 The “term value” T is the energy divided by hc . Thus . 1 1 . ) 4 ( 2 2 2 2 0 4 2 - πε μ = n hc e Z T h if the lowest level is taken to have zero energy, or The coefficient hc e 2 2 0 4 ) 4 ( 2 h πε μ is the Rydberg constant R for the hydrogen-like atom in question. (You may, if you wish, append a subscript to R to indicate which atom (e,g, Li ++ ) is under discussion.) Thus the term values are , 1 1 2 2 2 2 - - - = n RZ or n RZ T depending on where you take your zero to be. The quantity hc me 2 2 0 4 ) 4 ( 2 h πε is R , the Rydberg constant for a hydrogen atom of infinite nuclear mass , whose value, according to http://physics.nist.gov/cgi-bin/cuu/Value?ryd|search_for=rydberg+constant is 10 973 731.568 508 m -1
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10 H He + H α 2-3 656.278 nm 4-6 656.019 nm 4-7 541.160 Ηβ 2-4 486.133 4-8 485.940 4-9 454.166 Ηγ 2-5 434.047 4-10 433.874 4-11 419.990 Ηδ 2-6 410.174 4-12 410.010 2-3 164.2 Ly α 1-2 121.568 2-4 121.5 2-5 108.5 Ly β 1-3 102.583 2-6 102.5 2-7 99.2 Ly γ 1-4 97.254 2-8 97.2 2-9 95.9 The wavelengths that I have given for He + are approximate, because these lines show fine structure. The H lines also have some fine structure, but it is very fine indeed and difficult to observe. Note how every other line in He + coincides (nearly) with a line in H.
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9 1 2 3 2 3 4 5 6 1 H He +
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8 The energy levels of a hydrogenlike atom (referred to the ionization continuum as zero) are given by 2 2 2 0 4 2 1 . ) 4 ( 2 n e Z E h πε μ - = For hydrogen, Z = 1. For a hydrogen atom with infinite nuclear mass: 2 2 2 0 4 e 1 . ) 4 ( 2 n e m E h πε - = For a hydrogen atom with a proton for nucleus, 2 2 2 0 4 1 .
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