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