# Probablity density of 1s in hydrogen atom

1. Feb 12, 2010

### Karrar

I have two asks
In plot of probablity density of 1s electron of hydrogen atom
when r=0 where electron exist ?
is inside nucleus?! how happen this

what is the reduis of electron ri? and what reduis of nucleos RI is ? in Hamltonain operator
i mean the defination of r for (electron) and R for( nucleus)

2. Feb 12, 2010

### Bob S

Here is (I think) an estimate for the probability of the electron in a 1s hydrogen orbit being inside the proton (hydrogen nucleus).

The probability of the electon being "inside the proton" according to perturbation theory is (using Dirac notation)

P = <Re(r) l Rp(r) l Re(r)>

where Re(r) is the 1s electron radial wave function and Rp(r) is the proton radial charge distribution.

Using Re(r=0) = 2/a03/2

where a0 = Bohr radius and proton radius = Rp

we get

P = [STRIKE][4/a03][4 πRp3/3][/STRIKE] = [4/a03][Rp3/3]

Note that the probability is unitless. For muonic atoms, where a muon has replaced the electron in the 1s orbit, the muon in high-Z muonic atoms spends much of its time inside the nucleus.

Bob S

Last edited: Feb 12, 2010