C-46 Find the ratio of the time per...
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C-46 Find the ratio of the time period of 2- Bohr orbit of He' amd 4" Bohr orbit of Lj.

JEE/Engineering Exams
Chemistry
Solution
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Time taken ORbit [ T=frac{d i text { is }}{text { velocity }}=frac{2 pi r}{v} ] We know radius of Bohr's odit ( (gamma)=0-529 times frac{n^{2}}{2} ) A [ begin{aligned} &=0.529 times frac{n^{2}}{2} times 10^{10} end{aligned} ] [ begin{array}{l} text { & } bar{V}=2.188 times frac{z}{n} text { Aftes solving we get } T=1.52 times 10^{-16} times frac{n^{3}}{2^{2}} text { see } end{array} ] nud to find the ratio of time for the ( ^{+} quad n=2, quad z=2 ) fir ( operatorname{ci}^{2} t quad n=4, quad z=3 ) ( therefore ) ratio ( frac{pi}{T_{L i}^{2+}}=1.52 times 10^{16} times frac{(2)^{3}}{(2)^{2}} ) [ 1.52 times 10^{-16} timesleft(frac{4)^{3}}{(3)^{2}}right. ] ( =frac{8}{4} times frac{9}{648}=frac{9}{32} ) ". the ratio is 9: 32 ( Rightarrow quad frac{n^{3}}{22} mid ) for ontr ofher species / atoms
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