Angular momentum quantum numbers

In summary, the goal is to find an angular momentum quantum number l0 such that all states with l<l0 are bound, using the given potential V=(C/r3)-(D/r2). The conversation also includes a mention of the radial equation and a helpful PowerPoint resource.
  • #1
kcasali
12
0

Homework Statement


Remembering that a bound state exists if the effective potential is negative, find an angular momentum quantum number l0 such taht for all l<l0 the states are bound.

The given potential is V=(C/r3)-(D/r2), where C and D are positive numbers.

Homework Equations





The Attempt at a Solution



I don't even know where to start. I've been looking online for a few hours, I can't find anything even remotely helpful. Would I have to find an equation relating the radius to the quantum number, or am I way off track?
 
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  • #2
What's the effective potential equal to ? How does the radial equation look like ?
 
  • #3
dextercioby said:
What's the effective potential equal to ? How does the radial equation look like ?

I don't know if you're asking me if he gave any other equations (no, he didn't), or telling me I need those equations, haha.
 
  • #4
Nevermind, I found it. Thank you. :)
 
  • #5
I think this PowerPoint might help you. Good luck!

physics.wku.edu/~womble/phys480/lecture7.ppt
 

1. What is the purpose of the angular momentum quantum number in quantum mechanics?

The angular momentum quantum number, denoted by the letter l, is used to describe the shape of an electron's orbital in an atom. It helps to determine the possible values of the electron's orbital angular momentum and its energy level.

2. How is the angular momentum quantum number related to the principal quantum number?

The angular momentum quantum number is related to the principal quantum number, denoted by the letter n, in that it determines the sublevels within a given energy level. The value of l can range from 0 to n-1, meaning that there can be a maximum of n sublevels within an energy level.

3. What is the range of values for the angular momentum quantum number?

The angular momentum quantum number can have values ranging from 0 to n-1, where n is the principal quantum number. This means that for a given energy level, there can be a maximum of n sublevels with different values of l.

4. How does the angular momentum quantum number affect the energy of an electron?

The value of the angular momentum quantum number affects the energy of an electron by determining the shape of its orbital. Electrons with higher values of l have higher energies, as they have more orbits to cover within the same energy level. This also means that they are further away from the nucleus and experience less attraction, resulting in higher energy levels.

5. How does the angular momentum quantum number play a role in the periodic table?

The angular momentum quantum number plays a role in the periodic table by determining the sublevels within a given energy level. This is important because the sublevels determine the number of orbitals and the maximum number of electrons that can occupy each energy level. This ultimately affects the chemical properties and behavior of elements in the periodic table.

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