The electron in a hydrogen atom makes a transition n 1 → n 2 , where n 1 and n 2 are the principal quantum numbers of the two energy states. Assume the Bohr’s model to be valid. The time period of the electron in initial state is eight times that in the final state. What are the possible values of n 1 and n 2 ?
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. The expressions for velocity and radius of electron in nth orbit are
v n = 
… (1)
r n = r 0 n 2 … (2)
We can derive the expression for time period of
electron in nth orbit as,
T n = 
= 
= 
n 3 … (3)
Thus we can see that T n ∝ n 3 Hence, 
= 
… (4)
As T 1 = 8T 2 , from eqn. (4) we get 8 = 
or n 1 = 2n 2
Thus the possible values of n 1 and n 2 are
n 1 = 2, n 2 = 1; n 1 = 4, n 2 = 2; n 1 = 6, n 2 = 3 and so on.
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems