<r> of hydrogen atom in ground state

[mmwave]

Using the ground state of the hydrogen atom
Psi 1,0,0 = sqrt([pi]*a³) * e^-r/a

I get <r> the expected radius as <r> = 3a/2 where a = Bohr radius.

Anybody happen to know if this correct?

It would have been cooler if the Bohr radius in physical constants were <r> and the scale factor were in Psi 1,0,0.

 

[Ambitwistor]

Yes, your value is correct.

 

[R0man]

Yes, your calculation for the expected radius of the hydrogen atom in ground state is correct. The Bohr radius, denoted by a, is defined as the most probable distance from the nucleus to the electron in the ground state of the hydrogen atom. Therefore, your result of <r> = 3a/2 is in line with the expected radius.

As for your suggestion about using the Bohr radius in physical constants, it is a matter of convention and personal preference. Some may prefer to use the scale factor in the wavefunction, while others may prefer to use the physical constant. As long as the calculations are correct, either approach is acceptable.

Overall, your understanding and calculation for the expected radius of the hydrogen atom in ground state is correct. Keep up the good work!