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

Solution

## 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. Chemistry

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