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In an atom two electrons are moving in orbits of radii r and 9 r . The ratio of time taken by them to complete one revolution is Options: (a) 1:9 (b) 1:3 (c) 1:27 (d) 1:6

In an atom two electrons are moving in orbits of radii r and 9r. The ratio of time taken
by them to complete one revolution is
Options:
(a) 1:9
(b) 1:3
(c) 1:27
(d) 1:6
 

Grade:12

2 Answers

Aditya Gupta
2081 Points
4 years ago
v is inversely proportional to sqrt(R)
so, va/vb= sqrt(9/1)= 3
now, ta/tb= (2pi*r/va)/(2pi*(9r)/vb)
so, ta/tb= (r/va)*(vb/9r)
= (1/9)*(vb/va)
= 1/9 * 1/3
= 1/27
kindly approve :)
Vikas TU
14149 Points
4 years ago
Dear student 
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 = 9R
thus, the ratio of time taken will be
T1/T2 = (2πr1/v) / 2πr2/v  
or
T1/T2 = 2πR/2π(9R) = 2πR/18πR
thus.
T1/T2 = 1/9
Hope this information will clear your doubts about topic.
Good Luck 

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