Bohr/De-Broglie postulate

  • #1
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
 

Answers and Replies

  • #3
963
213
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.frequency


An 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
 

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