A few questions about the Bohr model

[Pseudo Statistic]

I was just doing some last minute review for my physics final tomorrow, and I have a few question about the Bohr model of the Hydrogen atom.

1) So at the ground state, a bound electron has -13.6eV energy. Now, say there was a photon with 14eV fired at it... would the electron escape?
I mean, I'm asking this because I hear that only discrete amounts of energy are accepted, and that a 12.5eV photon, for example, wouldn't be able to get the electron in the ground state to any other states because of quantization or something!
Can someone elaborate? (This totally confuses me)

2) I'm hearing things about deBroglie saying that electrons have to be standing waves or something? What does this mean?
I mean, I know that electrons have wave properties, according to deBroglie, and because of that the wavelength of each electron has to be an integer multiple of the circumference of its orbit, so that it doesn't interfere with itself. I don't know if that has anything to do with standing waves though...
Also, what about when you have 2 electrons in one energy level? How does that work?

3) Exactly how did the Franck Hertz experiment prove Bohr's model correct?

4) How exactly do we obtain the light spectra from atoms? Is it just a matter of exciting the electrons, allowing them to then go to some higher energy level, then come back down and break up the emitted light? (Which would mean that the observed frequencies of light would correspond to every possible energy level jump? e.g. from n=4 to n=1 would yield light of frequencies corresponding to jumps from 4->3, 4->2, 3->2, 3->1, 4->1, etc?)

Thanks for any responses.

 

[ZapperZ]

Yikes. Answering all your questions will take pages and pages. So I'll tackle the first one, and hopefully someone else will tackle the rest.

1) So at the ground state, a bound electron has -13.6eV energy. Now, say there was a photon with 14eV fired at it... would the electron escape?
I mean, I'm asking this because I hear that only discrete amounts of energy are accepted, and that a 12.5eV photon, for example, wouldn't be able to get the electron in the ground state to any other states because of quantization or something!
Can someone elaborate? (This totally confuses me)

It is only discrete when confined to the atom. The central potential of the atom causes the discrete energy level. In the "vacuum state" where an electron is free from that central potential, the energy level is continuous,i.e. all possible energy state is allowed. So yes, it can escape as long as it gains more energy than 13.6 eV, in principle.

Zz.

 

[jtbell]

I'll take #2.

According to the picture that most textbooks present, it seems to me that the condition that the circumference of the orbit equals a multiple of the wavelength can be satisfied either by a standing wave or by a traveling wave that moves around the circle at some speed. I don't remember whether de Broglie specifically had one kind of wave in mind.

The current model of the atom (based on the quantum-mechanical \Psi function and the Schrödinger equation) does use a standing wave, but it's a three-dimensional wave filling a spherical volume, rather than a one-dimensional wave going around in a circle.

Keep firmly in mind that neither the Bohr model nor de Broglie's original model look much like the current model of the atom. They were steps along the road to the current model, and they have serious flaws. For example, they predict that the electron must have nonzero orbital angular momentum, whereas "s states" (including the ground state of hydrogen) actually have zero orbital angular momentum!

They are important mainly for historical reasons: the Bohr model introduced the idea of quantized energy states, and de Broglie's model introduced the idea of "matter waves" which led to the quantum-mechanical \Psi function.

Anybody want to pick up from here with #3?

 

[StatMechGuy]

I'll take a crack at number (3)

The Frank-Hertz Experiment (two people) found that the energy levels of an atom are discrete. So what did they do?

Taking a gas of mercury, they used an electron gun to fire the electrons into the gas, controlling their kinetic energy. They then measured the kinetic energy of the electrons after shooting through the gas. What they found was that there were periodic dips depending on the applied voltage to the electrons (ie their kinetic energy), which seemed to indicate that when the electrons elastically scattered with the mercury atoms, only discrete amounts of energy were transferred. If you buy the picture of the atom that there is a large electron cloud surrounding a tiny nucleus, most of the collision occurred with the electron cloud, so this seems to make a comment about the outermost electrons.

 

[ZapperZ]

Wow! We make quite a team!

:)

Zz.