Calculating Electron Probability in a Cone

[dinospamoni]

Homework Statement

Consider an electron in the n = 5, ℓ = 2, mℓ = -1 state.
What is the probability that the electron is located in a cone
of half angle 41◦ about the z axis? (In other words, what is the
probability that θ ≤ 41◦
?)

Homework Equations

P=∫∫∫R(r)^2 * Y[θ,phi]^2

The Attempt at a Solution

I'm not quite sure what I'm doing here, but this is as far as I got:

I said R(r) is a constant because the angle doesn't depend on the radius.

Next I found an expression for Y(theta,phi) from my textbook based on l and m_l:

Y(θ,f)=.5*sqrt(15/2pi)SinθCosθ * e^-i*f

I integrated Y^2, .7156<θ<pi, 0<f<pi

This probability is not right.

ANy ideas?

 

[Simon Bridge]

You have assumed the radial wavefunction is a constant for that state... did you check, say, by looking it up or computing it? Did you remember to take the complex conjugate for the complex parts of the wavefunction?