Probability of finding an electron

[stunner5000pt]

Homework Statement

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

Homework Equations

$$\int_{all space} \Psi^*(r') \Psi(r') dr'$$

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??

 

[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.

 

[stunner5000pt]

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.

doesnt the radial density matter as well??

 

[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.