The probability of finding the electron at radius r is given by P(r) = r²|Rn1(r)|², where Rni(r) is the radial wavefunction. a) Explain where the r² term comes from in the expression for the probability above. b) Look up (or calculate if you really want to!) and write down the radial wavefunctions for n = 1,2,3 and all allowed values of l.
The probability of finding the electron at radius r is given by P(r) = r²|Rn1(r)|², where Rni(r) is the radial wavefunction. a) Explain where the r² term comes from in the expression for the probability above. b) Look up (or calculate if you really want to!) and write down the radial wavefunctions for n = 1,2,3 and all allowed values of l.
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Transcribed Image Text:2. The probability of finding the electron at radius r is given by P(r) = r²|Rn1(r)P,
where Rni(r) is the radial wavefunction.
a) Explain where the r² term comes from in the expression for the probability
above.
b) Look up (or calculate if you really want to!) and write down the radial
wavefunctions for n = 1,2, 3 and all allowed values of l.
c) Plot the probability distributions (i.e.
you wrote down above. Plot them all on the same graph, so you will need to
label the graph in some way to identify which line is which.
P(r)) for each of the wavefunctions
Hint: the quickest way would to be use Python and mathplotlib which you
learned about in PH370 last year. However, if you didn't take PH370 last
year (or just don’t like python), then feel free to use any tool you normally
use for plotting graphs, e.g. in lab modules.
d) Comment on any trends you see in the graphs you plotted in the previous
section.
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