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endeavor
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Homework Statement
The wave function of an electron in the lowest (that is, ground) state of the hydrogen atom is
[tex]\psi(r) = (\frac{1}{\pi a_0^3})^{1/2} exp(-\frac{r}{a_0})[/tex]
[tex]a_0 = 0.529 \times 10^{-10} m[/tex]
(a) What is the probability of finding the electron inside a sphere of volume 1.0 pm3, centered at the nucleus (1pm = 10-12m)?
(b) What is the probability of finding the electron in a volume of 1.0 pm3 at a distance of 52.9 pm from the nucleus, in a fixed but arbitrary direction?
(c) What is the probability of finding the electron in a spherical shell of 1.0 pm thickness, at a distance of 52.9 pm from the nucleus?
Homework Equations
[tex]|\psi(r)|^2[/tex]
The Attempt at a Solution
(a) [tex] volume = 1.0 \times 10^{-36} m^3[/tex]
using r = 0, the probability is 1.137 * 10-16.
(b), (c) What equations should I use here?
[tex]R^2|\psi(r)|^2[/tex] ?
[tex]4\pi r^2 R^2|\psi(r)|^2[/tex] ?
but I don't have R...