What Can the Wave Function for Hydrogen Tell Us About Its Properties?

In summary, the conversation discusses a hydrogen atom in the 2s state and its wave function. The given wave function is used to calculate its value at r=a_o, which is 0.0529 nm. The question is raised about the meaning of this value, and it is explained that wave functions are primarily used as a calculational tool in determining observable quantities.
  • #1
jg370
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Homework Statement



Suppose a hydrogen atom is in the [tex]2s[/tex] stat, with its wav function given by:

[tex]\psi_2_s (r) = \frac{1}{4\sqrt(2\pi a_o^\frac{3}{2})} (2-\frac{r}{a_o}) e^(-\frac{r}{2a_o})[/tex]

Taking [tex]r = a_o[/tex], calculate [tex]\psi_2_s (a_o)[/tex]

Homework Equations




The Attempt at a Solution



Since [tex]r=a_o=0.0529 nm[/tex], I get [tex]\frac{1.57*10^(14)}{ m^3}[/tex]

Now, my question is "what is the meaning of this value?
 
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  • #2
Well, the units of a 3-D wave function should have m3/2 in the denominator (i.e. the units are m-3/2).

I'm not sure people actually ascribe physical meaning to the value of a wavefunction. I think of wavefunctions as a calculational tool in determining observable quantities such as position, momentum, energy, etc. QM is all about measurable quantities or observables.

Hope that helps.
 

1. What is the wave function for hydrogen?

The wave function for hydrogen is a mathematical expression that describes the probability of finding an electron in a specific location around a hydrogen atom. It takes into account the energy of the electron, the distance from the nucleus, and the orientation of the electron's spin.

2. How is the wave function for hydrogen calculated?

The wave function for hydrogen is calculated using Schrödinger's equation, which is a differential equation that takes into account the physical properties of the electron, such as its mass and charge, and the forces acting on it, such as the attractive force from the nucleus. The solution to this equation gives the wave function.

3. What is the significance of the wave function for hydrogen?

The wave function for hydrogen is significant because it provides a complete description of the electron's behavior in a hydrogen atom. It allows us to calculate the probability of the electron being in a particular location, which is important for understanding the atomic structure and chemical properties of hydrogen.

4. How does the wave function for hydrogen change with different energy levels?

The wave function for hydrogen changes with different energy levels by adjusting the shape and size of the electron's probability distribution. Higher energy levels have more nodes and a larger average distance from the nucleus, while lower energy levels have fewer nodes and a smaller average distance from the nucleus.

5. Can the wave function for hydrogen be visualized?

Yes, the wave function for hydrogen can be visualized using various mathematical representations, such as contour plots or 3D graphs. These visualizations show the electron's probability of being in different regions of space around the hydrogen atom, giving us a better understanding of its behavior.

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