To explain the Bohr Atom Energy Levels for the Hydrogen Atom, De Broglie postulated that an electron orbiting the proton nucleus of the Hydrogen Atom would only occupy discrete orbits due to the wave nature of the electron. What de Broglie hypothesised was that for each orbit, the circumference could only be of a length equal to an integral number of wavelengths.
De Broglie was theorising that each orbit corresponded to a whole number of wavelengths.
The ground state should have a circumference of one electron wavelength: n = 1.
The first excited state would have two electron wavelengths fitted into it: n = 2.
The second excited state would have a length equal to three electron wavelengths: n = 3: and so on.
De Broglie was drawing on the understanding of sound waves and musical instruments such as stringed instruments, where it was known that standing waves are set up when a stringed instrument vibrates. Each octave in the musical scale corresponds to an integral number of wavelengths in a standing wave.
Einstein was interested in de Broglie's postulate and asked Schrodinger to analyse it from a mathematical perspective.
Schrodinger then postulated that an electron has a wave function and developed an equation from which he established a solution.
Developing a solution to his equation was easiest for a simple atom such as the Hydrogen atom. Schrodinger's solution showed remarkable consistency with the Bohr atom energy levels.
The energy levels of hydrogen, as calculated by Schrodinger are given by
where n = 1 for the ground state, n=2 is the first excited state, n = 3 is the second excited state etc.
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