In an atom, two electrons moves around the nucleus in circular orbit of radius R and

4R.Calculate the ratio of time taken to complete one revolution around the nucleus.

time taken to complete a single revolution

T = path distance / velocity

or

T = 2πr/v  (1)

here we assume that the linear velocity remains constant i every orbit.

so,

T1 = 2πr1/v  (2)

where r1 = R

and

T2 = 2πr2/v  (3)

where

r2 = 4R

 

thus, the ratio of time taken will be

T1/T2 = (2πr1/v) / 2πr2/v  

or

T1/T2 = 2πR/2π(4R) = 2πR/8πR

thus.

 

T1/T2 = 1/8

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