- #1

blaksheep423

- 18

- 0

## Homework Statement

The ground state (lowest energy) radial wave function for an electron bound to a proton to form a hydrogen atom is given by the 1s (n=1, l=0) wave function:

R

_{10}= (2 / a

^{3/2}) exp(-r / a)

where r is the distance of the electron from the proton and a is a constant.

a) Sketch the wave function, and

b) What is the expectation value of <r

^{2}> for the electron?

## Homework Equations

i think the equation for <r

^{2}> is

[tex]\int[/tex] R*r

^{2}R dr

from -infinity to infinity

## The Attempt at a Solution

for a) i am completely blanking on how to sketch the wave function. for b) i was able to use an integral table to evaluate <r

^{2}> and i got 8 / [tex]\sqrt{}a[/tex]

however, i have a feeling that my original equation for <r

^{2}> is wrong, and should involve some sort of Y and [tex]\phi[/tex] and [tex]\Theta[/tex]

also, should i be integrating from 0 - a, or -infinity to infinity?