# Do really the electrons could only orbit in specific orbits with a fixed radius?

According to Bohr's model of atom

The electrons could only orbit the nucleus in specific orbits or shells with a fixed radius. Only shells with a radius given by the equation below would be allowed, and the electron could not exist in between these shells.
r(n)=n​2 ​​ ⋅r(1)

But when I learnt about different orbitals inside the atom in my textbook, it was said that you cannot precisely tell the location of an electron, as you know the velocity, according to Heisenberg's uncertainty principle. Besides in a video of khanacademy.org Sal said that orbitals means that if we took a number of snapshots of atoms, we would see that the electrons are denser in those orbitals but that does not necessarily mean that we wouldn't find it outside of the orbitals. The probability of finding electrons is higher in the orbitals but not 100%. But Bohr said electrons are quantized. It must be in a fixed orbital with a fixed radius. Isn't that contradictory? Which one is true? Or what is wrong in my understanding?

## 1 Answer

Bohr said electrons are quantized. It must be in a fixed Orbital with a fixed radius. Isn't that contradictory?

No it is not contradictory.

"Quantized" means that a continuous range of a variable, such as energy, is not allowed. Only discrete values of the variable are allowed.

In Bohr's model, the radii and energies were quantized.

Which one is true?

It is not true that electrons orbit in fixed circular orbits. Subsequent to the Bohr theory, there was Sommerfeld theory, which involved elliptical orbits and was a relativistic theory that correctly predicted the fine structure of the hydrogen atom (which Bohr's theory did not). Then there was Schrodinger's theory, which did away with the fixed orbits, but was non-relativistic and gave the same energy levels as Bohr's theory. This was followed by Dirac's theory which was a relativistic theory and gave the same energy levels as Sommerfeld's theory. However, the hyperfine structure of the hydrogen atom, such as the Lamb shift, was still not explained, until quantum electrodynamics was developed. Further developments included the recognition that the proton is not a point particle, but is composite. So there has been no finding the truth, just more accurate, but more complex, approximations of the truth.

Sal said that orbitals means that if we took a number of snapshots of atoms, we would see that the electrons are denser in those orbitals but that does not necessarily mean that we wouldn't find it outside of the orbitals. The probability of finding electrons is higher in the orbitals but not 100%

Orbitals have an infinite spatial extent. There are nodes where the wavefunction is zero for the Schrodinger equation solutions of the hydrogen atom, but nodes are specific planes, conical surfaces or spherical surfaces, not 3-dimensional regions. People depict the orbitals as having finite volumes, but these depictions are the high probability regions not the entire orbital. So if Sal said that, he should have said that the electrons can be outside of the high-probability regions of orbitals that people draw, rather than saying outside the orbitals.