- #1
leroyjenkens
- 616
- 49
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
[tex]P_{nl}(r) = r^{2}|R_{nl}(r)|^{2}[/tex]
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 [itex]R_{10}(r)[/itex], which is [itex]\frac{2}{(a_{0})^{\frac{3}{2}}}e^{\frac{-r}{a_{0}}}[/itex]
I just square that whole thing and get [itex]\frac{4e^{\frac{-2r}{a_{0}}}}{(a_{0})^{3}}[/itex]
I know the value of [itex]a_{0}[/itex], but I'm not sure what r is. Is r the radius, which happens to be the same as the Bohr radius ([itex]a_{0}[/itex]) for this problem?
I want to be able to calculate an actual number instead of having an answer with variables in it.
Thanks.