Question

Ionisation energy of $ H{e^ + } $ is $ 19.6 \times {10^{ - 18}}Jato{m^{ - 1}} $ . The energy of the first stationary state (n=1) of $ L{i^{2 + }} $ is:
(A) $ 4.4 \times {10^{ - 16}}Jato{m^{ - 1}} $
(B) $ - 4.41 \times {10^{ - 17}}Jato{m^{ - 1}} $
(C) $ 2.2 \times {10^{ - 15}}Jato{m^{ - 1}} $
(D) $ 8.82 \times {10^{ - 17}}Jato{m^{ - 1}} $

Answer 1

Hint: Bohr recommended that electrons don't emanate energy as they circle the core, yet exist in conditions of steady energy which he called fixed states. This implies that the electrons circle in fixed good ways from the core. Bohr's work was basically founded on the discharge spectra of hydrogen.

Complete Step By Step Solution:
Bohr clarified that electrons can be moved into various circles with the expansion of energy. At the point when the energy is taken out, the electrons return back to their ground state, emanating a comparing measure of energy – a quantum of light, or photon. This was the reason for what later got known as quantum hypothesis. This is a hypothesis dependent on the rule that issue and energy have the properties of the two particles and waves. It represents a wide scope of actual wonders, including the presence of discrete parcels of energy and matter, the vulnerability guideline, and the rejection standard.
Since,
 $ \left( {\dfrac{{I{E_{L{i^{2 + }}}}}}{{I{E_{H{e^ + }}}}}} \right) $ = $ \left( {\dfrac{{{Z_{L{i^{2 + }}}}}}{{{Z_{H{e^ + }}}}}} \right) $ = $ {9 \mathord{\left/
 {\vphantom {9 4}} \right.} 4} $
 $ \Rightarrow I{E_{L{i^{2 + }}}} = \dfrac{9}{4} \times I{E_{H{e^ + }}} = \dfrac{9}{4} \times 19.6 \times {10^{ - 18}} $
And that is equal to $ 4.41 \times {10^{ - 17}}J/atom $
Energy in stationary state = −IE = $ 4.41 \times {10^{ - 17}}J/atom $ .

Additional Information:
Following the disclosures of hydrogen emanation spectra and the photoelectric impact, the Danish physicist Niels Bohr $ \left( {1885-1962} \right) $ proposed another model of the particle in $ 1915 $ . Bohr suggested that electrons don't transmit energy as they circle the core, however they exist in conditions of consistent energy which he called fixed states. This implies that the electrons circle in fixed good ways from the core. Bohr's work was principally founded on the discharge spectra of hydrogen. This is likewise alluded to as the planetary model of the particle. It clarified the internal functions of the hydrogen iota. Bohr was granted the Nobel Prize in material science in $ 1922 $ for his work.

Note:
Bohr's work affected our cutting-edge comprehension of the inward activities of the molecule. Nonetheless, his model functioned admirably for a clarification for the outflows of the hydrogen iota, yet was genuinely restricted when applied to different particles. Soon after Bohr distributed his planetary model of the molecule, a few new revelations were made, which came about in, once more, a reconsidered perspective on the iota.