| Probability for a Range of Radius | 
|  | Finding the probability that the electron in the hydrogen ground state will be found in the range r=b to r=c requires the integration of the radial probability density.  | 
This requires integration by parts. The form of the solution is

| Radial behavior of ground state | Most probable radius | 
| Expectation value for radius | 
| HyperPhysics***** Quantum Physics | R Nave |