8-10 - 8­10 In high­temperature sources, sodium atoms...

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Unformatted text preview: 8­10 In high­temperature sources, sodium atoms emit a doublet with an average wavelength of 1139nm. The transition responsible is from the 4s to 3p state. Set up a spreadsheet to calculate the ratio of the number of excited atoms in the 4s state to the number in the ground 3s state over the temperature range from an acetylene oxygen flame (3000 oC) to the hottest part of an inductively coupled plasma source (8750 oC) 1 v= = 8779cm −1 −7 1139nm * 10 cm / nm E j = 8779cm −1 * 1.986 * 10 −23 Jcm = 1.743 * 10 −19 J The statistical weights for the 3p and 4s quantum states: 3 1 + 1 + 2 * + 1 = 6 3p: 2 * 2 2 3 2 + 1 + 2 * + 1 = 5.2 4s: 2 * 5 2 gj 5.2 = = 0.87 So g0 6 Substituting into equation 8­1 yields (for temp = 3000 oC) = 0.87 * e = 0.0184 N0 Substituting into equation 8­1 yields (for temp = 8750 oC) Nj N0 = 0.87 * e −1.743*10 −19 J 1.38*10−23 J / K *(8750 + 273)K Nj −1.743*10−19 J 1.38*10−23 J / K *(3000 + 273)K = 0.215 ...
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