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**1. 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 pm

^{3}, centered at the nucleus (1pm = 10

^{-12}m)?

(b) What is the probability of finding the electron in a volume of 1.0 pm

^{3}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?

**2. Homework Equations**

[tex]|\psi(r)|^2[/tex]

**3. 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...