A How are energy levels and De-Broglie wavelengths related in the Bohr model?

[blackdranzer]

From the Bohr/De Broglie postulate we have n λ = 2πr where λ is the De-Broglie wavelength , r is the radius corresponding to n and n is the quantum number.

1. An electron in the state n=2 has more energy than that at n=1
2. That implies that the De- Broglie wavelength associated with the electron should also decrease ?

From the postulate..it is the other way i.e. the wavelength increases as the electron gains energy. How is this possible?.( I had assumed that wavelength decreases with energy)

if we calculate the De-Broglie wavelengths from the postulate:

for n=1 ; λ = 33 * 10^-11 m

for n=2 ; λ = 66 * 10^-11 m

does this mean that as the energy of the electron increases the corresponding De-Broglie wavelength increases?! may be i am missing something very basic here.

semiclassical

 

[blue_leaf77]

Bohr postulate is outdated. Nevertheless if you want to know the behavior of the wavelengths for different quantum number n, you must transform the wavefunction into momentum space. It's not an easy task though, for example in hydrogen atom see http://forum.sci.ccny.cuny.edu/Members/lombardi/publications/MOMREP-H-atom.pdf/view.

 

[drvrm]

does this mean that as the energy of the electron increases the corresponding De-Broglie wavelength increases?! may be i am missing something very basic here.

Bohr's condition, that the angular momentum is an integer multiple of h/2.pi was later reinterpreted in 1924 by de Broglie as a standing wave condition: the electron is described by a wave and a whole number of wavelengths must fit along the circumference of the electron's orbit:

however the atom model is bound state model and in each orbit the particles total energy must be negative (sum of KE + PE) and the lowest orbit is the deepest and slowly it goes towards zero ...i.e. the particle becomes free.
say for hydrogen atom the ionization energy is 13.6 ev .
so the ground state n=1 is at -13.6 eV. so higher states will be closer to zero and the number will be smaller...
so how one can see it ...
say -13.6 eV is larger or smaller than -10 eV ?
one has to supply +3.6 eV to the electron to raise it to -10 eV.
and if an emission has taken place by transfer of electron from say E2 to E1 then E2 - E1 =h.frequencyAn electron in the lowest energy level of hydrogen (n = 1) therefore has about 13.6 eV less energy than a motionless electron infinitely far from the nucleus. The next energy level (n = 2) is −3.4 eV. The third (n = 3) is −1.51 eV, and so on. For larger values of n, these are also the binding energies of a highly excited atom with one electron in a large circular orbit around the rest of the atom.
see wikipedia <https://en.wikipedia.org/wiki/Bohr_model#Origin> for detail discussion