## Homework Statement

Determine the most probable radius of an electron for a 2s hydrogenic atom.

## Homework Equations

r*=a0/Z where a0 is Bohr radius

## The Attempt at a Solution

Well, I know that the answer is ~5.2a0/Z. The book tells me that the most probable radius for hydrogen (EDIT - a 2s hydrogen shell I mean) is 5.2a0 - thus I know that the answer is simply 5.2a0/Z (275pm/Z) for the series of hydrogenic atoms. My only problem is this: I don't know how to get the coefficient of 5.2, and presumably simply getting it out of the book is not the right way to do it. I think it may have to do with taking the derivative of the wavefunction but I'm unsure...Any help would be appreciated, thanks!

G01
Homework Helper
Gold Member
The probability for an electron to be found in the radial range r+dr can be determined using the wavefunction for the 2S state:

$$P(r+dr)=|\Psi_{200}|^24\pi r^2dr$$

Now if you want to find the most probable value, your looking for the value of r, such that P(r+dr) is a maximum. Think back to calculus. What is the condition for a function, P(r) to be maximum?

HINT: The condition involves $$\frac{dP}{dr}$$