Question

The electron in a hydrogen atom makes a transition n1 n2 , where n1 and n2 are the principal quantum numbers of two states. Assume the bohrs model to be valid. The time period of the electron in the initial state is eight times that in the final state. The possible values of n1 and n2 are

Answer 1

let the time period in initial state is T1

and the time period in final state is T2

T1 = 8T2 (given in question)

as we know that....

Time period is directly proportional to n^3

we can write, T = k n^3

where k is constant.....

Now,

T1 = kn1^3. .........1) T2=kn2^3 ......2)

divide equation 1 and 2.......

8T2/T2 = kn1^3/kn2^3

8/1 = (n1/n2)^3

n1/n2 = 2/ 1

so n1=2 and n2 = 1