Quantum Chemistry/Example 20

Write an example showing the determination of the initial electronic state of the hydrogen atom given the wavelength of its transition to the ground state.

==<Example 20>==Edit

An electronic transition of H atom from an energy level to the ground state is observed with a corresponding wavelength of 102.5 nm. Determine the initial state of the electron from which transition has occurred.Edit

The Rydberg's phenomenological equation will be used to solve the energy transition problem

Rydberg's phenomenological equation for hydrogen

 

where the   is Rydberg constant for hydrogen and is equal to 109737  .   is the final energy level,   is the initial energy level for hydrogen transition. Both   and   are integers and  .


The wavelength is given as 103nm

Concert to SI units:

 


The H atom's transition is from unknown energy level to the ground state.

So we can know the final state is the ground state which means  


The   now can be calculated:

 

 

 


Because the energy level always  

 

Therefore, the initial state of the electron from which transition has occurred is energy level 3.