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Bohr's Model of Hydrogen Atom
Concepts tested here
- Energy of Bohr orbits
All Questions
2005 AIPMT 1 question
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The energy of second Bohr orbit of the hydrogen atom is $-328$ kJ mol$^{-1}$; hence the energy of fourth Bohr orbit would be :-Energy of the $n$th Bohr orbit: $E_n \propto -\dfrac{1}{n^2}$
$\dfrac{E_4}{E_2} = \dfrac{n_2^2}{n_4^2} = \dfrac{2^2}{4^2} = \dfrac{4}{16} = \dfrac{1}{4}$
$E_4 = \dfrac{E_2}{4} = \dfrac{-328}{4}$
$E_4 = -82$ kJ mol$^{-1}$
(Check: $E_1 = -1312$ kJ mol$^{-1}$, so $E_4 = \dfrac{-1312}{16} = -82$ kJ mol$^{-1}$.)