Question

An isolated atom of a certain element emits light of wavelength 512 nm when the atom falls from its fifth excited state into its second excited state. The atom emits a photon of wavelength 411 nm when it drops from its sixth excited state into its second excited state. Find the wavelength of the light radiated when the atom makes a transition from its sixth to its fifth excited state.

An isolated atom of a certain element emits light of wavelength 512 nrm when the atom alls from its fifth excited state into its second excited state. The atom emits a photon of wavelength 411 nm when it drops Trom its sixth excited state into its second exted state. Find tha wavelength of the light radiated when the atom makes ה transition fram its sixth to its fifth excited state. excited st exoted

Answer 1

Given that E_5 similarto E_2 implies 512 nm and E_6 similarto E_2 implies 411 nm According to quantization rules, E_6 - E_2 = (E_6 - E_5) + (E_5 - E_2) Therefore, the wavelength of light radiated from sixth to fifth transition found as follows: 1/lambda_62 = 1/lambda_65 + 1/lambda_52 (because E = hc/lambda) 1/lambda_65 = 1/lambda_62 - 1/lambda_52 implies 1/lambda_65 = lambda_62 times lambda_52/lambda_52 - lambda_62 we get, lambda_65 = 411 times 512/(512 - 411) nm implies lambda_65 = 2083.4851 nm