# Bohr Model missing momentum question

• ianbell

#### ianbell

In the Bohr atomic model, electrons move between shells having angular momentum L_n = n h_bar where n is the shell number and the difference in shell energies E_n2-E_n1 matches the Rydberg energy of the emitted or absorbed photon.

My question is: what hapened to the angular momentum (n2-n1)h_bar?

For this to be carried in or out by the "massless" photon (assuming we abandon Bohr classicism for relativistic 4-vector momentae) would require the photon trajectory to be at a precisely correct angle.

Of course.

"Of course"? You mean that's the theory? An incoming photon already of precisely absorbable wavelength just happens to have precisely the right trajectory to provide the necessary angular momentum too?? What are the odds?

If the atom was scattering photons it might be more credable but isn't the electron is supposed to "absorb" the photon to acquire all its energy?

Furthermore, the constuction of the Bohr model to provide the Rydberg formula seems to neglect the change in kinetic energy when moving from one orbit to another. Or have I missed something?

hit the electron at precisely the right point in its orb

In the Bohr atomic model, electrons move between shells having angular momentum L_n = n h_bar where n is the shell number and the difference in shell energies E_n2-E_n1 matches the Rydberg energy of the emitted or absorbed photon.

My question is: what hapened to the angular momentum (n2-n1)h_bar?

For this to be carried in or out by the "massless" photon (assuming we abandon Bohr classicism for relativistic 4-vector momentae) would require the photon trajectory to be at a precisely correct angle.
The intensity of the emitted radiation varies as |P_L(cos\theta)|^2 where L is the angular momentum of the emitted photon. (This is for a 100% polarized atom).

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But if the electron is absorbing a photon to gain energy, why should this photon have precisely the correct mementum too? If it sheds surplus momentum by emitting a photon, it will lose energy.

Why shouldn't it have precisely the correct momentum? Remember this is the Bohr model...

"Why shouldn't it have precisely the correct momentum?"

Because its just not credable. This is angular momentum so the photon has to have /exactly/ the right trajectory. The absence of consideration of orbital kinetic energy alarms me too.

This is the Bohr model. There's a reason it isn't used anymore: it's very, very wrong.

This is angular momentum so the photon has to have /exactly/ the right trajectory.

Er, yes? The Bohr model is semiclassical, so this fits. I'm not sure what your problem with this is.