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The energy of the electron in hydrogen atom is known to be expressible in the form E_(n) = - (13.6)/(n^(2)) eV (n = 1,2,3,…..). Use this expressionto show thatthe . (i) electron in the hydrogen atom cannot have an energy of -2 eV.(ii) spacing between the lines (consecutive energy levels) within the given set of the observed hydrogen spectrum decreases as increases. |
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Answer» Solution :(i) From the relation`E_(N) =- (13.6)/(n^(2))eV`,we have . `E_(1) = - (13.6)/((1)^(2)) = - 13.6eV,"" E_(2) = - (13.6)/((2)^(2)) = - 3.4 eV` `E_(3) =- (13.6)/((3)^(2)) = - 1.51 eV,""E_(4) = - (13.6)/((4)^(2)) = - 0.85 eV` andso on...... Thus , it is very MUCH clear the electron in thehydrogenatomcannot havean energyof -2eV. (iii) Energydifferencebetweenconsecutiveenergylevelsis : `Delta E_(1) = E_(2)- E_(1) = - 3.4 - (-13.6) eV = 10.2eV` `Delta E_(2) =- E_(3) - E_(2) = -1.51 - (-3.4) eV = 1.89 eV` `Delta E_(4) -E_(3) = - 0.85- (-1.51) eV = 0.66 `eV and so on. Thus, ITIS clear thatspacingbetween the lines within the GIVEN set of observedhydrogenspectrumdecreases as n increases. |
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