leroyjenkens
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Homework Statement
What is the probability that an electron in the ground state of hydrogen is within one Bohr radius of the nucleus?
Homework Equations
P_{nl}(r) = r^{2}|R_{nl}(r)|^{2}
The Attempt at a Solution
Since it's an electron in the ground state of a hydrogen atom, that means n = 1, and that means it's in the s orbital, which means l = 0.
So using the formula provided in the book for R_{10}(r), which is \frac{2}{(a_{0})^{\frac{3}{2}}}e^{\frac{-r}{a_{0}}}
I just square that whole thing and get \frac{4e^{\frac{-2r}{a_{0}}}}{(a_{0})^{3}}
I know the value of a_{0}, but I'm not sure what r is. Is r the radius, which happens to be the same as the Bohr radius (a_{0}) for this problem?
I want to be able to calculate an actual number instead of having an answer with variables in it.
Thanks.