# A few questions about the Bohr model

• Pseudo Statistic
In summary, during a conversation about the Bohr model of the Hydrogen atom, various questions were raised about its implications and connections to other theories. These included inquiries about the behavior of bound electrons under different energy levels, the role of standing waves in de Broglie's model, the accuracy of the Bohr model, and the significance of the Franck Hertz experiment in proving the correctness of the Bohr model. The conversation also delved into the process of obtaining light spectra from atoms and its relation to energy level jumps.

#### 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.

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.

Pseudo Statistic said:
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.

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?

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.

Wow! We make quite a team!

:)

Zz.

## What is the Bohr model?

The Bohr model is a simplified representation of the atomic structure proposed by physicist Niels Bohr in 1913. It describes the atom as having a small, positively charged nucleus surrounded by negatively charged electrons in specific energy levels or orbits.

## How does the Bohr model explain atomic spectra?

The Bohr model explains atomic spectra by proposing that electrons can only exist in specific energy levels and can move between these levels by absorbing or emitting energy in the form of light. The different energy levels correspond to specific wavelengths of light, which can be observed as distinct lines in the atomic spectrum.

## Is the Bohr model still considered accurate?

While the Bohr model was groundbreaking at the time, it has been superseded by more complex models such as the quantum mechanical model. However, it is still used as a simplified representation of atomic structure in introductory chemistry courses.

## What are the limitations of the Bohr model?

The Bohr model has several limitations, including its inability to accurately predict the spectra of atoms with more than one electron, its assumption that electrons move in circular orbits, and its failure to account for the wave-like behavior of electrons.

## How did the Bohr model contribute to our understanding of atomic structure?

The Bohr model was a significant step in our understanding of atomic structure, as it was the first model to propose that electrons occupy specific energy levels rather than moving randomly around the nucleus. It also helped to explain the observed atomic spectra and laid the foundation for further developments in quantum mechanics.