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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 \dots .

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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