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**1. Homework Statement**

Hey Guys!

Here's my problem: ψ=2(Z/a)^3/2*e^ρ/2 for the 1s orbital of a hydrogen atom. Write down the radial distribution function expression (P) of a 1s electron and determine the most likely radius.

ρ=2Zr/a

Z nuclear charge

r radius

a Bohr's radius

**2. Homework Equations**

P=(ψ*)(ψ)∂τ= 4(Z/a)^3*e^ρ*4π*r^2*∂r

**3. The Attempt at a Solution**

We need to calculate ∂P/∂r

My professor solves r=a/Z which is all well and fine, but in an intermediate step he goes from P=(stuff)*e^(-2Zr/a)*r^2*∂r to ∂P/∂r=∂/∂r((stuff)*e^(-2Zr/a)*r^2)

To me it seems that he has neglected a ∂r and it should read ∂P/∂r=∂/∂r((stuff)*e^(-2Zr/a)*r^2*∂r), in which case I am not sure how to calculate something like this.

What would help me solve this is to know if I am making some stupid mistake, or if there is some rule in the form x=y∂r ---> ∂x=∂(y∂r)=? (my guess would be ∂x=∂y∂r+y(∂^2)r, but this doesn't agree with my professor's tricks, and I haven't taken a PDE class to know my way around)

Thanks guys!