Question

Is Lambda one is the wavelength of the photon emitted by the electron when it jumps from third Orbit to first Orbit and Lambda 2 is the wavelength of the photon emitted by the electron when it jumps from third Orbit to second orbit and Lambda 3 is the wavelength of the photon emitted by the electron when it jumps from orbit second to orbit first derive a relation between Lambda 1 Lambda 2 and Lambda 3

Answer 1

Rydberg's equation will allow to calculate the wavelength of the photon emitted by the electron during transition

1/λ=R⋅(1/n^2.final−1/n^2.initial), where

λ - the wavelength of the emitted photon;
R - Rydberg's constant - 1.0974⋅107m−1;

since first transaction is from n=3 to n=1
so, 1/Lambda1=R(1/1^2 -1/3^2)....(1)
2nd transaction is from n=3 to n=2
so, 1/Lambda2=R(1/2^2 -1/3^2).....(2)
3rd transaction is from n=2 to n=1
so 1/Lambda3=R(1/1^2 -1/2^2)....(3)
now add eqn (2) &(3)
So, 1/Lambda2 +1/Lambda3
=R(1/2^2 -1/3^2 +1/1^2 -1/2^2)
=R(1/1^2 -1/3^2)
=1/Lambda1
So, 1/Lambda2 +1/Lambda3 =1/Lambda1
This is the relation.