mass of quantum states

[James R]

Jason.Marshall:

I made an algebraic error in post #11. I am sorry that I said your formula didn't produce the values it produces. It does. Let's take a look.

You start with
$$\pi \left( \frac{r}{H} \right)^2 = a$$
When r=1, a=2, from which it follows, as you say, that
$$H=\sqrt{\frac{\pi}{2}}$$
Plugging this value of H back into the initial formula, we have:
$$\pi \times \left( r\sqrt{\frac{2}{\pi}} \right)^2 = a \Rightarrow a=2r^2$$
As it happens, the number of electrons that can fit in an atomic shell with principal quantum number $$n$$ is $$2n^2$$, which is a result from quantum mechanics. Your formula $$a=2r^2$$ is algebraically equivalent, so of course it produces the same sequence 2,8,18,32,...

Now, you wrote:

I already have my own way to calculate the maximum of electrons that can fit the orbitals of s,p,d,f ...

and indeed you have a mathematical expression that produces the correct value.

But it still remains for you to explain the theory that relates your mathematical formula to the electron structure of atoms. What, in your mathematics, predicts that atoms will have orbitals s,p,d,f etc? How are electrons arranged in those orbitals? Can you explain that?

And what exactly are r and a in your formula? What, physically, do those variables represent?

 

[origin]

Jason.Marshall:

I made an algebraic error in post #11. I am sorry that I said your formula didn't produce the values it produces. It does. Let's take a look.

You start with
$$\pi \left( \frac{r}{H} \right)^2 = a$$
When r=1, a=2, from which it follows, as you say, that
$$H=\sqrt{\frac{\pi}{2}}$$
Plugging this value of H back into the initial formula, we have:
$$\pi \times \left( r\sqrt{\frac{2}{\pi}} \right)^2 = a \Rightarrow a=2r^2$$
As it happens, the number of electrons that can fit in an atomic shell with principal quantum number $$n$$ is $$2n^2$$, which is a result from quantum mechanics. Your formula $$a=2r^2$$ is algebraically equivalent, so of course it produces the same sequence 2,8,18,32,...

Now, you wrote:

and indeed you have a mathematical expression that produces the correct value.

But it still remains for you to explain the theory that relates your mathematical formula to the electron structure of atoms. What, in your mathematics, predicts that atoms will have orbitals s,p,d,f etc? How are electrons arranged in those orbitals? Can you explain that?

And what exactly are r and a in your formula? What, physically, do those variables represent?

JM seems to be one of these numerology fellows that takes a result that a real scientist discovered and then make up an arbitrary equation that gets to that number. Of course the arbitrary equation has no basis in a physical process.

 

[Jason.Marshall]

"But it still remains for you to explain the theory that relates your mathematical formula to the electron structure of atoms. What, in your mathematics, predicts that atoms will have orbitals s,p,d,f etc? How are electrons arranged in those orbitals? Can you explain that?"

"And what exactly are r and a in your formula? What, physically, do those variables represent?"[/QUOTE] r is for radius value and a is for area values I have not isolated the exact reason this is connected to chemistry its just an arbitrary true fact that I notice but I will be conducting more extensive investigations for I assume it has something to with the mass gap problem.

You have to remember James I just started working on this theory 2 to 3 weeks ago I am still investigating and building my theory so I can submit it for peer review then get it published. But its basically the solution for the "Quadrature of a circle" and also a counterexample for the "Reimann hypothesis". As I continue to develop it I can determine new relationships as I go progress is still not thouroghly determined yet.