Review Questions

1. What are the three Einstein coefficients and explain what each represents and quantifies. What are the Einstein relations and what is there utility?

2. The oscillator strength is conveniently defined to be a unitless quantity that is in proportion to the Einstein A coefficient. What important transition properties does the oscillator strength quantify? 

3. Consider Equation 21.17, which is written for transition in the Schrödinger atomic model. What do we call the terms gnl and gn'l' ? What do these quantities physically represent? Equation 21.17 informs us that the oscillator strengths for spontaneous emission transition nl -> n'l' is not equal to the oscillator strength for the absorption transition n'l' -> nl between the two same levels, but that they are in proportion to the g values of the upper and lower states. Explain why this is.

4. In words, what is a radial overlap integral an integration of? What is the range of integration? Considering Equation 21. 15, what quantity is the radial overlap integral providing once it is computed (in other words, what is the interpretation of the expression, or value, that results from the integration)?

5. Consider an s-p fine structure doublet with transitions s1/2 - p1/2 and s1/2 - p3/2. For example, for hydrogenic ions, this could be the Ly⍺ doublet or any other Lyman-series doublet for that matter. Of these doublet members, which transition has the larger oscillator strength? How many times larger is it than the other transition in the doublet? So, what do expect for the relative strength of these two fine-structure doublets when observed in a spectrum?

6. Provide a qualitative description of why a transition energy of a given emission or absorption line is "fuzzy" and not always the exact same value, thus there is a phenomenon called "natural line broadening". Consider Figure 21.7, when computing the damping constant, Γ (the e-folding time of a spontaneous transition), why do the all the decay channels of both the upper state and the lower state need to be considered in the calculation?

7. What is the name of the famous mathematical function that describes the line broadening function? In this function, what does the damping constant,  Γ, physically represent in terms of the shape of the broadened emission or absorption line? 

8. At this point, we see that every transition is characterized by three "atomic constants".  What are these three constants? (HINT: they give the line center, the line strength, and the line width.)

9. What is an absorption cross section? What are the units of the absorption cross section (use cgs!)? 

10. Qualitatively describe the bound-bound cross section for Ly⍺ (see Figure 21.9). What governs its shape and approximately how many angströms wide is its FHWM?  Qualitatively describe the continuous bound-free (ionization) cross section for ionization of a hydrogen from its ground state (see Figure 21.10). Why does it have a sharp cut off, or edge?

Problems

1. Under construction