Probablity density of 1s in hydrogen atom

[Karrar]

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

second ask
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)

 

[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 = <R_e(r) l R_p(r) l R_e(r)>

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

Using R_e(r=0) = 2/a₀^3/2

where a₀ = Bohr radius and proton radius = R_p

we get

P = [STRIKE][4/a₀³][4 πR_p³/3][/STRIKE] = [4/a₀³][R_p³/3]

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