# Proof using mainly classical mechanics

• physicsjock
In summary: I've been trying to differentiate it but it keeps giving me errors.In summary, the first equation looks like it would be the most useful to use, but the h and n come from different sources and the n is derived from the Ritz principle and Rydbergs formula. If you're only using classical ideas, the n and h come from the ionization energy.
physicsjock
Hey,

http://img822.imageshack.us/img822/407/25944209.jpg
\begin{align} & \frac{m{{v}^{2}}}{r}=\frac{Z{{e}^{2}}}{4\pi {{\varepsilon }_{0}}{{r}^{2}}} \\ & L=\frac{Z{{e}^{2}}}{4\pi {{\varepsilon }_{0}}v} \\ \end{align}

and I know by using the v derived using Bohr's equations it will give the answer but that v is derived using L=nh so it's not that simple.

I can't figure out how to quantize L without breeching the conditions of the question. Would anyone have any ideas?

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You want to quantise L without using any premises of quantum mechanics?

Haha, that's what's messing this up for me, that's how I've been thinking, I don't see how you can get a result like that using means that don't agree with the result.

There's a few results I just found which I can use,

$E=-\frac{hR}{{{n}^{2}}};\frac{{{\left| E \right|}^{3}}}{{{\omega }^{2}}}=\frac{{{Z}^{2}}m{{\alpha }^{4}}}{8}=\frac{R{{h}^{3}}}{16{{\pi }^{2}}}=\operatorname{Constant},\alpha =\frac{{{e}^{2}}}{4\pi {{\varepsilon }_{0}}}$

At first glance the first equation looks like the most useful but h and n and inversely related, and I can't shake the squared on the n.

If you're using only classical ideas, where did the n and the h come from in E?

It was derived using Ritz principal and Rydbergs formula

${{E}_{n}}-{{E}_{m}}=h\,{{v}_{nm}}$

λ-1=$R\left( \frac{1}{{{m}^{2}}}-\frac{1}{{{n}^{2}}} \right)$

So I'm trying to find a way to quantize L using classical mechanics in conjunction with the results I posted before

I'm having trouble deriving

$E=-\frac{hR}{{{n}^{2}}}$

as well,

This is what I've been doing,
\begin{align} & \frac{1}{\lambda }=R\left( \frac{1}{{{m}^{2}}}-\frac{1}{{{n}^{2}}} \right) \\ & \frac{ch}{\lambda }=vh=E=chR\left( \frac{1}{{{m}^{2}}}-\frac{1}{{{n}^{2}}} \right) \\ & E=-chR\left( \frac{1}{{{n}^{2}}} \right) \\ \end{align}

It's supposed to be the ionization energy, so the 1/m disappears because you take the limit as m -> infinity

Not sure how to get rid of the c

## 1. What is classical mechanics?

Classical mechanics is a branch of physics that studies the motion of macroscopic objects, such as particles, rigid bodies, and fluids. It is based on Newton's laws of motion and the principles of conservation of energy and momentum.

## 2. How is classical mechanics used in scientific research?

Classical mechanics is used to understand and predict the behavior of physical systems, such as the motion of planets, the behavior of fluids, and the properties of materials. It is also used to design and analyze machines and structures, such as bridges and airplanes.

## 3. Can classical mechanics explain all physical phenomena?

No, classical mechanics has its limitations and cannot fully explain certain phenomena, such as the behavior of particles at the atomic and subatomic level. For these situations, quantum mechanics is needed.

## 4. What are some commonly used mathematical tools in classical mechanics?

Some commonly used mathematical tools in classical mechanics include calculus, vector algebra, differential equations, and Newton's laws of motion. These tools are used to describe and analyze the behavior of physical systems.

## 5. How has classical mechanics influenced other branches of science?

Classical mechanics has had a major impact on other branches of science, such as engineering, astronomy, and chemistry. It has provided a foundation for understanding the physical world and has led to the development of new technologies and advancements in various fields.

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