If an electron from a hydrogen like atom with Z=2 jumps from the 4^ th orbit to the 2^ nd orbit, it emits a photon of wavelength . What is the wavelength of the photon emitted if an electron jumps from the 5^ th orbit to the 4^ th orbit?

Step-by-step solution

The wavelength of a photon emitted during a transition from orbit n₂ to n₁ in a hydrogen-like atom with atomic number Z is given by the Rydberg formula: 1 = R Z^2 ( 1 n₁^2 - 1 n₂^2 ) For the first case, Z=2 , n₁=2 , and n₂=4 . Substituting these values: 1 = R (2)^2 ( 1 2^2 - 1 4^2 ) = 4R ( 1 4 - 1 16 ) = 4R ( 4-1 16 ) = 4R ( 3 16 ) = 3R 4 Thus, = 4 3R . For the second case, Z=2 , n₁=4 , and n₂=5 . Let the wavelength be ' . 1 ' = R (2)^2 ( 1 4^2 - 1 5^2 ) = 4R ( 1 16 - 1 25 ) = 4R ( 25-16 400 ) = 4R ( 9 400 ) = 9R 1