Question

Q. In an atom two electrons move around the nucleus in circular orbits of radius R and 4 R .calculate the ratio of the time taken by them to complete one revolution .​

Answer 1

Answer:

Hola! ✨✨✨✨

We have,

A - electron with radius 'R'

B - electron with radius '4R'

v α 1/√R

=> v(A) α 1/√R

& v(B) α 1/√4R => v(B) α 1/2√R

Their ratio :

v(A)/v(B) = (1/√R) * (2√R/1)

v(A)/v(B) = 2

Now,

To find : Ratio of time taken

i.e. t(A)/t(B) = ?

Since,

t = 2πR/v

Therefore,

t(A)/t(B) = [2πR/v(A)]/[2π(4R)/v(B)]

t(A)/t(B) = (1/4)*(vB/vA)

t(A)/t(B) = (1/4)*(1/2)

t(A)/t(B) = 1/8

OR

t(A) : t(B) = 1 : 8

Answer 2

.•♫•heya •♫•.

T = 2πr/ v

but

R is directly proportional to n square .

V inversely proportional to n .

T ^2 is directly proportional to (n)^3

T^2 is directly proportional to r^3

T is directly proportional to r^3/2

T1/T2 = (r1/r2)^3/2

= 1/ 8