The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is equal to ${{{h^2}} \over {xma_0^2}}$. The value of 10x is ___________. (a0 is radius of Bohr's orbit) (Nearest integer) [Given : $\pi$ = 3.14]
Answer (integer)
3155
Solution
$mvr = {{nh} \over {2\pi }}$<br><br>$$K.E. = {{{n^2}{h^2}} \over {8{\pi ^2}m{r^2}}} = {{4{h^2}} \over {8{\pi ^2}m{{(4{a_0})}^2}}}$$<br><br>$= \left( {{4 \over {8{\pi ^2} \times 16}}} \right){{{h^2}} \over {ma_0^2}}$<br><br>$\Rightarrow$ x = 315.507<br><br>$\Rightarrow$ 10x = 3155 (nearest integer)
About this question
Subject: Chemistry · Chapter: Atomic Structure · Topic: Bohr's Model
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