Atomic Hydrogen: Solving Homework on Thanksgiving - Help Needed

[MadPhys]

I spent my Thanksgiving trying to solve my homework and I will need some help:

1)For fixed electron energy ,the orbital quantum number l is limited to n-1.We can obtain this result from a semiclassical argument using the fact that the larges angular momentum describes circular orbits,where all kinetic energy is in orbital form.For hydrogen-like atoms U(x)=-(Zke^2)/r
and the energy in circular orbits becomes:

E=((|L|^2)/2mr^2)-(Zke^2)/r

Quantize this realtion using the rules of |L|=(l(l+1))^0.5 and E=-((ke^2)Z^2)/(2an^2),together with the Bohr result for the allowed values of r,to show that the largest integer value of l consistent with total energy i s lmax=n-1


solution:

ke^2)Z^2)/(2an^2)=((|L|^2)/2mr^2)-(Zke^2)/r and substituting |L|=(l(l+1))^0.5


ke^2)Z^2)/(2an^2)=(l(l+1))/2mr^2)-(Zke^2)/r

but i don't know what to do after this

please can somebody help me

 

[dextercioby]

You have to substitute for the r versus n dependence as given by Bohr.

Daniel.

 

[MadPhys]

When I use formula for Bohrs radius

my equation is :

n=(l(l+1))^05

and i don't know how i can from here get

lmax=n-1

 

[dextercioby]

You should have gotten an inequation. See if l_max=n will fit into your equation.

Daniel.