Time-averaged potential of hydrogen

In summary, the conversation is about finding the charge distribution that will give a specific potential for a neutral hydrogen atom. The potential is given by a formula with a term for the Bohr radius and a term for the proton. The solution involves finding the electric field and taking its divergence to find the charge density.
  • #1
cscott
782
1

Homework Statement



The time-averaged potential of a neutral hydrogen atom is given by

[tex]V = \frac{q}{4 \pi \epsilon_0} \frac{e^{-\alpha r}}{r} \left ( 1 + \frac{\alpha r}{2} \right )[/tex]

[tex]\alpha = 2/a_0[/itex], where [itex]a_0[/itex] is the Bohr radius.

Find the charge distribution (continuous and discrete) which will give you this potential.

The Attempt at a Solution



Totally stuck here except I think the charge density of the |1s> state should be

[tex]\rho = e<1s|1s>[/itex],

however that doesn't get me very far. Is the second term in V the contribution of the proton?
 
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  • #2
There's no need to think about quantum mechanics here. This is just a classical electromagnetics problem. You have a potential. Find the corresponding electric field and then take its divergence to find the charge density.
 

Related to Time-averaged potential of hydrogen

What is the time-averaged potential of hydrogen?

The time-averaged potential of hydrogen refers to the average potential energy of a hydrogen atom over a given period of time. It takes into account the fluctuations in the potential energy as the atom moves and interacts with its surroundings.

Why is the time-averaged potential of hydrogen important in chemistry?

The time-averaged potential of hydrogen is important in chemistry because it helps predict the behavior and reactivity of hydrogen atoms in different environments. It also provides insight into the stability and bonding of hydrogen molecules.

How is the time-averaged potential of hydrogen calculated?

The time-averaged potential of hydrogen is calculated by taking the average of the potential energy values at different points in time. This can be done using mathematical equations or through computer simulations.

What factors affect the time-averaged potential of hydrogen?

The time-averaged potential of hydrogen can be affected by factors such as temperature, pressure, and the presence of other atoms or molecules. Changes in these conditions can alter the potential energy and therefore impact the overall average.

What are the applications of understanding the time-averaged potential of hydrogen?

Understanding the time-averaged potential of hydrogen has many applications in fields such as materials science, biochemistry, and astrophysics. It can help in the development of new materials, understanding chemical reactions, and studying the behavior of hydrogen in different environments.

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