In an atom two electrons move round the nucleus in circular orbits of radii R and 4R respectively. The ratio of the time taken by them to complete one revolution is

Question

espex · Answer

If the one orbit is 4 times the length of the first, it seems that it would be a 1:4 ratio.

anonymous · Answer

it is 1:8

espex · Answer

Because it is a radius..

hoblos · Answer

you must find the ratio of the parameters

anonymous · Answer

t^2 ~r^3

espex · Answer

hoblos: Could you elaborate please.

anonymous · Answer

square of the time period directly proportional to the cube of the radius

espex · Answer

That is for planetary orbits which electrons do not mimic. I was under the impression it was a probability function that defined electron orbits.

anonymous · Answer

Assuming that they move with the same speed then hoblos is right because the time taken for 1 revolution is directly porportional to the perimeter of the circular paths. therefore the perimeter of the electron with radii R is $$2\pi r$$
and the perimeter of the other electron is $$2\pi(4R)=8\pi r$$

Therefore,

$$8\pi r:2\pi r=4$$