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In the Bohr atom model, the frequency of transitions is given by the following expression v=Rc(1/n^(2)-1/m^(2)), where nltm, Consider the following transitions: Show that the frequency of these transitions obey sum rule (which is known as Ritz combination principle) |
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Answer» Solution :In the Bohr ATOM model, the frequency of transition `upsilon = R_(c) ((1)/(N^(2)) - (1)/(m^(2)))n lt m ` `I^(st)` transition, m = 3 and n = 2 `upsilon_(3) to 2 = R_(c) ((1)/(2^(2)) - (1)/(3^(2))) = R_(c) ((1)/(4)- (1)/(9)) ` `= R_(c) ((9-4)/(36)) = R_(c) ((5)/(36))` `II^(nd)` transition , m = 2 and n = 1 `upsilon _(2) to 1 R_(c) ((1)/(1^(2))-(1)/(2^(2))) = R_(c) (1 - (1)/(4)) = R_(c) ((3)/(4))` `III^(rd)` transition m = 3 and n = 1 `upsilon _(3) to1 = R_(c) ((1)/(1^(2)) - (1)/(3^(2))) = R_(c)(1-(1)/(9)) = R_(c) ((8)/(9))` According to Ritz combination principle, the frequency transition of single STEP is the sum OFFREQUENCY transition in two steps. `upsilon_((3) to 2) + upsilon_((2) to 1) = upsilon_((3) to 1)` `R_(c) ((5)/(36)) + R_(c) ((3)/(4)) = R_(c) ((8)/(9))` `R_(c) ((8)/(9)) = R_(c) ((8)/(9))` `upsilon_((3) to 2)+ upsilon_((2) to 1) = upsilon_((3) to 1)` |
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