how can i derive a formula to calculate the speed of an electron in n^(th) orbit of a hydrogen atom?


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Question Number 50451 by JDlix last updated on 16/Dec/18

$h o w c a n i d e r i v e a f o r m u l a t o c a l c u l a t e t h e s p e e d o f a n e l e c t r o n$ $i n n^{t h} o r b i t o f a h y d r o g e n a t o m ?$
	Answered by tanmay.chaudhury50@gmail.com last updated on 16/Dec/18

	$\frac{1}{4 π ϵ_{0}} \frac{e \times e}{r_{n}^{2}} = \frac{{m v}^{2}}{r_{n}}$ $a n g u l a r m o m e n t u m = {m v r}_{n} = \frac{n h}{2 π}$ ${m v}^{2} r_{n} = {k e}^{2} e q n 1 [k = \frac{1}{4 π ϵ_{0}}]$ ${m v r}_{n} = \frac{n h}{2 π} e q n 2$ $d e v i d i n g e q n 1 b y e q n 2$ $v = \frac{{k e}^{2}}{n h} \times 2 π$ $v = \frac{1}{4 π ϵ_{0}} \times \frac{e^{2}}{n h} \times 2 π = \frac{e^{2}}{2 ϵ_{0} h} \times \frac{1}{n}$ $p l s c h e c k . . . .$
	Commented by peter frank last updated on 16/Dec/18

	$y o u r r i g h t i g e t t h e s a m e$ $r e s u l t$
	Answered by peter frank last updated on 16/Dec/18

	Commented by JDlix last updated on 17/Dec/18

	$i w a n t t o t h a n k b o t h o f u$
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