Consider an electron within the 11s orbital of a hydrogen atom. The normalized probability of finding the electron within a sphere of a radius R centered at the nucleus is given by
normalized probability=120[20−−20(20+20+22)]normalized probability=1a02[a02−e−2Ra0(a02+2a0R+2R2)]
where 0a0 is the Bohr radius. For a hydrogen atom, 0=0.529 Åa0=0.529 Å. What is the probability of finding an electron within one Bohr radius of the nucleus?
Why is the probability of finding the electron at the Bohr radius not equal to 1?
The electron may exist at a range of radii. The Bohr radius is the average distance of the electron from the nucleus.
The electron may exist at a range of radii. The Bohr radius is at the highest probability density.
The electron may exist at a range of radii. The Bohr radius is just the radius at which there is an equal probability of finding the electron inside the radius as outside.
The electron may exist at a range of radii. The Bohr radius is only the most probable distance of the electron from the nucleus.
What is the probability of finding an electron of the hydrogen atom within a 1.7501.75a0 radius of the hydrogen nucleus?