Solving Hydrogen Atom Equations for l & a and Finding Energy]

[Eilerson]

Homework Statement

Find the values of l and a for which the function R(r) = Cexp[-r/a], where C and a are constants, is a solution of the radial equation for the hydrogen atom.

Then find the energy in terms of the rydberg constant and the magnitude of the angular momentum. Finally state the spectrospic name (eg 1s) of the electron.

Homework Equations

The Attempt at a Solution

So I substituted R(r) = u(r)/r and got to here (see attached). I assume I'm supposed to compare coefficients but this leaves me with the columb term floating there. Any hints?

[

 

[nrqed]

Homework Statement

Find the values of l and a for which the function R(r) = Cexp[-r/a], where C and a are constants, is a solution of the radial equation for the hydrogen atom.

Then find the energy in terms of the rydberg constant and the magnitude of the angular momentum. Finally state the spectrospic name (eg 1s) of the electron.

Homework Equations

The Attempt at a Solution

So I substituted R(r) = u(r)/r and got to here (see attached). I assume I'm supposed to compare coefficients but this leaves me with the columb term floating there. Any hints?

[

Homework Statement

Homework Equations

The Attempt at a Solution

I am confused. You say R = c e(-r/a) here but in your attachment you use r e^(-r/a).

In addition, in your attachment, if we use the R given there, u(r) should be r^2 e^(-r/a)

 

[Eilerson]

Oops yeah, messed up at the start. I'll have another go and report back.

 

[nrqed]

Oops yeah, messed up at the start. I'll have another go and report back.

I am sure it will work now.

 

[Eilerson]

This looks better.