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If an orbital...

Question

If an orbital electron of the hydrogen atom jumps from the ground state to higher energy state, its orbital speed reduces to half its initial value. If the radius of the electron orbit in the ground state is $r$ , then the radius of the new orbit would be:

A

2 r

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B

4 r

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C

8 r

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D

16 r

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Solution

The correct option is B $4 r$
$t h e r a d i u s o f n t h o r b i t i s p r o p o r t i o n a l t o n^{2} a n d t h e v e l o c i t y i n t h e n t h o r b i t i s i n v e r s e l y p r o p o r t i o n a l t o n t h e e l e c t r o n j u m p s f r o m t h e g r o u n d s t a t e t o a s t a t e n s u c h t h a t i t s v e l o c i t y d e c r e a s e s t o i t s h a l f t h e r e f o r e n = 2 N o w r a d i u s b e c o m e s n^{2} r = 4 r$ \quad

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