# Homework Help: Probability of finding an electron

1. Jan 30, 2007

### stunner5000pt

1. The problem statement, all variables and given/known data
Consider the probability of finding an electron in the region defined by the cone of half angle 23.5 degrees measured from the z axis

a) If the electron were eqally likely to be found anywhere in space, then what would be the proability of finding it inside the cone?

b) Repeat the same calcuculation but for an electron in a n=2, l=1, m=0 state

2. Relevant equations
$$\int_{all space} \Psi^*(r') \Psi(r') dr'$$
3. The attempt at a solution

for part a do they mean the electron in the ground state $\Psi_{000}$??

In whiuch case the integral we need to do is

$$\int_{0}^{\0}^{\infty} (rR_{00}(r))^2 dr \int_{0}^{\frac{47\pi}{360}} \int_{0}^{\pi} (Y_{00}(\theta,\phi})^2 \sin \theta d\theta d\phi$$

And apply the similar concept to get the answer for part b??

2. Jan 30, 2007

### Meir Achuz

Part A means to put in a WF that is a constant.
The answer is then just the solid angle of the 23.5 degree cone.
For part B, put Y_{10}^2 into the integral.

3. Jan 30, 2007

### stunner5000pt

doesnt the radial density matter as well??

4. Feb 1, 2007

### Meir Achuz

The radial integral is the same for the cone as for all solid angle, so it does not affect the ratio of the two integrals.