Need help fast Radial probablility density in ground state hydrogen

In summary, the conversation discusses a person's request for help with determining the radial dependence of probability density for the ground state of the one electron hydrogen atom. They reference two sources, one stating that the radial dependence is P(r)dr = |\psi|^2 4 \pi r^2 dr, while the other shows a different equation. The person asks for an explanation as to why there is a discrepancy between the two equations.
  • #1
Whazupp
8
0
I'm working all alone with nobody to help me, and now I'm stuck! :(

I'd really appreciate it if you could help me out. I'm working with the ground state of the one electron hydrogen atom. Trying to determine the radial dependence on probability density. It should only depend on the radial coordinate and not on the other spherical coordinates.

I've got one book saying the the radial dependence of probability density is:

[tex]P(r)dr = |\psi|^2 4 \pi r^2 dr[/tex]

Now another says something along the lines of:

http://img222.imageshack.us/img222/5153/radialic9.jpg

I got these two from:

http://phy.asu.edu/phy361-alarcon/FALL06/lecture22_1109.ppt" (power point)

and

https://www.physicsforums.com/showthread.php?t=49807"

Now why aren't they the same? Please help.
 
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  • #2
We need to see your reasoning first.

Start with the probability density - how is it defined?
 

FAQ: Need help fast Radial probablility density in ground state hydrogen

1. What is the radial probability density in the ground state of hydrogen?

The radial probability density in the ground state of hydrogen is a measure of the probability of finding the electron at a certain distance from the nucleus. It is given by the equation P(r) = (4 / a)^3 * r^2 * e^(-2r/a), where a is the Bohr radius.

2. How is the radial probability density related to the electron's energy in the ground state of hydrogen?

The radial probability density is directly proportional to the electron's energy in the ground state of hydrogen. This means that as the probability density increases, so does the energy of the electron.

3. What does the graph of the radial probability density in the ground state of hydrogen look like?

The graph of the radial probability density in the ground state of hydrogen is shaped like a bell curve, with the peak at the nucleus and the probability decreasing as the distance from the nucleus increases.

4. How does the ground state radial probability density differ from other energy states in hydrogen?

The ground state radial probability density is unique in that it has the highest probability of finding the electron at a certain distance from the nucleus. As the energy level increases, the probability density decreases and the shape of the curve changes.

5. Why is the ground state radial probability density in hydrogen important?

The ground state radial probability density is important because it provides valuable information about the behavior of electrons in atoms. It helps us understand the distribution of electrons in the atom and how they interact with the nucleus.

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