What is the ratio of energies in a hydrogen atom and how can it be calculated?

[Erwin Kreyszig]

[SOLVED] Energies of a Hydrogen Atom

1. I have a question on the ratio of energies of an electron in a hydrogen atom. It seems quite simple, but yet seem to be struggling...can anyone help?
2. The question is: "calculate the most probable value of the electron-orbit radius, r, and the ratio of the electron kinetic energy to its potential energy in the ground state of the hydrogen atom"
3. So far i have found the most probable value of the electrons orbit radius, by taking the |[tex]\Psi[/tex]|^2 and multiplying it by the volume element, all in spherical polars. What i am struggling on is the ratio of the energies.

Thanks EK

 

[Mr.Brown]

For the kinetic Energies just take the kinetic part of the hamiltonian as a kinetic energy operator ?

 

[malawi_glenn]

Q1:
It depends on what level you should do this problem.

The general formula for hydrogenic atom energy levels are very simple and you should know that one by heart. Or should you be able to derive it?

The energy levels are proportional to [tex] n^{-2} [/tex], does this look familiar?

 

[Erwin Kreyszig]

Thanks guys, so as it is in the ground state this solution is even easier, it is just taking the K.E operator and putting it over the potential (the attractive force on the electron) Thanks for all your help

EK

 

[Erwin Kreyszig]

For the kinetic Energies just take the kinetic part of the hamiltonian as a kinetic energy operator ?

So i can use the K.E from the Hamiltonian, and use the potential as the coulomb interaction between the electron and the proton, then equate the ratio from those?

Thanks EK

 

[Mr.Brown]

Yeah just calculate the kinetic energy with the KE operator.
Then calculate the mean radius of that given wave function put that in coulombs formula and equate the ratio :)

 

[Erwin Kreyszig]

Yeah just calculate the kinetic energy with the KE operator.
Then calculate the mean radius of that given wave function put that in coulombs formula and equate the ratio :)

Perfect, thanks for all your help.

EK

 

[Erwin Kreyszig]

Yeah just calculate the kinetic energy with the KE operator.
Then calculate the mean radius of that given wave function put that in coulombs formula and equate the ratio :)

I am obviously being dumb here, but how can i calculate the kinetic energy using the KE operator? What is it operating on? Do i chose a probable wave function, i.e. guess at it being and exponential, for example, e^-cr, and operate on that?

Thanks

EK

 

[Erwin Kreyszig]

Yeah just calculate the kinetic energy with the KE operator.
Then calculate the mean radius of that given wave function put that in coulombs formula and equate the ratio :)

Sorry to be retarded, but to find the potential then you have to find the expectation value of the ground state radius, which is the Bohr radius yes? Then you sub that Bohr radius into the coulombs law and that is your Potential?
Then equate then with that i can find my ratio of the two energies?


EK