Question

1. Draw out a diagram for the first 10 energy levels of the hydrogen atom. Compare and contrast these with our other model systems (particle in a box, harmonic oscillator, rigid rotor).
2. Calculate the energy difference between the first two levels of the hydrogen atom. What part of the electromagnetic spectrum would this occur in?
3. Look at the radial distribution functions (you can easily find these on line or in any pchem text) and develop a rule about the number of radial nodes based on quantum number(s).   
4. A certain hydrogen line atom (with only 1 electron) emits light with a frequency of 2.2 x10¹⁶ Hz from n=2 to n=1. What frequency of light will be emitted from n=3 to n=2?
5. Write an expression for the average position, r, for an electron in the 1s orbital of hydrogen.
6. Solve for the radial nodes of a 3s orbital for a hydrogen atom.

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3. Look at the radial distribution functions (you can easily find these on line or in any pchem text) and develop a rule about the number of radial nodes based on quantum number(s).   

The number of radial nodes is equal to the number of total nodes minus the number of angular nodes. The total number of nodes is n-1, where n is the principal quantum number and number of angular modes is equal to l – the angular quantum number, so the rule can be n-l-1, that gives the number of radial nodes....

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