Why don't scientists define the atomic radius as the radius of its electron cloud?

Answer 1

An electron cloud does not have a specific radius -- it is in fact a probability distribution.

An analogy is the atmosphere. What is the radius of the atmosphere? You can't give one number because there is no dividing line where the atmosphere exist on one side but doesn't on the other. Instead, it just gets thinner and thinner and thinner... (see the Related Questions to the left for more about the sky).

You can meaningfully talk about a radius that includes a percentage of the total. For instance, you can say that at some radius, you will find the electron inside that radius 95% percent of the time. But if you picked the radius where it would be 99% of the time inside, it would be much larger. To have the percentage be exactly 100%, the radius would be infinite!

Because of this complication, atomic radii are usually determined by the distance between to atoms when they are in a bond together -- and is taken to be approximately half the distance between the two nuclei (although it is slightly more complicated than that in fact).

Answer 2

The electron probability density gradually drops as you move further from the nucleus, but it never quite goes to zero, so you'd need to choose a more or less arbitrary limiting value to decide where the cloud "ended." It makes a lot more sense to define the radius as something with an actual physical meaning, such as the point where the potential between two atoms switches from attractive to repulsive.

Answer 3

Scientists don't define the atomic radius as the radius of the electron cloud because the electron cloud is not a well-defined boundary. It is a probabilistic region where the electrons are likely to be found. Instead, the atomic radius is defined as half the distance between the nuclei of two bonded atoms in a molecule.

Answer 4

The atomic radius is defined: covalent, ionc, Van der Waals radius.