[Alext180]

Although electrons are almost massless, and therefore the electron cloud is also almost massless, could it be said that it is dense due to the measure of "electron density" being how probable it is for an electron to occur in a certain area? Considering the electron cloud is the area more highly populated with electrons, it seems that the electron density would be quite high. So, is the electron cloud dense?

[Arkcon]

It hard to be specific in cases such as this but, no I don't think so.  Consider hydrogen:  it has 1 s electron in a spherical orbit.  We define the electron cloud as a probability of finding an electron there.  But there is still just one..  So there's two for helium, but that's it.  Likewise for other elements and sub-orbitals -- there's at most 2 in each case.

[insertwittyname]

The way I understand it, the electron cloud is said to be dense if the probability of finding an electron in the area under consideration is high. For example, in the p-orbital, the density is maximum in the lobes but zero at the node. Thus the probability of finding an electron in the p-orbital is maximum in the lobes and zero at the node.
Hope that this helps, Cheers!

[antimatter101]

It is not density in mass or volume, it is density in electric charge.

[Borek]

In the electron cloud mass density is directly proportional to the charge density, it is as simple as that.

[Alext180]

So if the charge density is proportional to the mass density, and the charge density is very high, its mass density must also be very high

[Corribus]

Why not roughly estimate it?

Consider hydrogen.  There is one electron and in the ground state the electron is in a 1s orbital.  The wavefunction extends out to infinity so in principle the density is zero because the electron is spread over an infinite volume, but let's put an upper limit on it. Arbitrarily I will say that the electron is confined to a sphere of radius 3.147896 times the Bohr radius, which is where an electron in a 1s hydrogen orbital will be found 95% of the time. I calculated this by integrating the radial probability distribution and setting it equal to 0.95, solving for distance from the nucleus in factors of Bohr radius.

Anyway, the volume of space enclosed by 3.147896 Bohr radii is 1.934 X 10^-29 cubic meters.  The mass of an electron is 9.109382 x 10^-31 kg. Therefore the density is estimated to be 0.0471 kg/m³. (You can neglect volume of the nucleus, which is incredibly small comparably).

This calculation is quite crude but it should at least give you a feel for scale. For comparison, the density of water in the same units is about 997 kg/m³, over 21,000 times larger. In fairness, hydrogen is a rather light atom.  What about something like lead? Well, a lead atom has 82 electrons. So is the density of electrons in lead 82 times that of hydrogen? Not really, because those electrons are forced into more diffuse orbitals which are spread out over larger volumes. For example, an electron in a hydrogen 3d orbital has an estimated mass density (taking a crude determination of confining to a shell ranging from 4 to 18 Bohr radii, and still working with hydrogenic wavefunctions) of about 0.0002547 kg/m³. Given that the real density of lead in solid form is 11340 kg/m³, this should show you that almost all of the density of solid matter comes from the nuclei.

[Alext180]

Why not roughly estimate it?

Consider hydrogen.  There is one electron and in the ground state the electron is in a 1s orbital.  The wavefunction extends out to infinity so in principle the density is zero because the electron is spread over an infinite volume, but let's put an upper limit on it. Arbitrarily I will say that the electron is confined to a sphere of radius 3.147896 times the Bohr radius, which is where an electron in a 1s hydrogen orbital will be found 95% of the time. I calculated this by integrating the radial probability distribution and setting it equal to 0.95, solving for distance from the nucleus in factors of Bohr radius.

Anyway, the volume of space enclosed by 3.147896 Bohr radii is 1.934 X 10^-29 cubic meters.  The mass of an electron is 9.109382 x 10^-31 kg. Therefore the density is estimated to be 0.0471 kg/m³. (You can neglect volume of the nucleus, which is incredibly small comparably).

This calculation is quite crude but it should at least give you a feel for scale. For comparison, the density of water in the same units is about 997 kg/m³, over 21,000 times larger. In fairness, hydrogen is a rather light atom.  What about something like lead? Well, a lead atom has 82 electrons. So is the density of electrons in lead 82 times that of hydrogen? Not really, because those electrons are forced into more diffuse orbitals which are spread out over larger volumes. For example, an electron in a hydrogen 3d orbital has an estimated mass density (taking a crude determination of confining to a shell ranging from 4 to 18 Bohr radii, and still working with hydrogenic wavefunctions) of about 0.0002547 kg/m³. Given that the real density of lead in solid form is 11340 kg/m³, this should show you that almost all of the density of solid matter comes from the nuclei.

Well we know that the nucleus contains most of the mass of the atom, but I think we can say that the electron cloud is also dense because of its charge density?

[Borek]

I think we can say that the electron cloud is also dense because of its charge density?

Define "dense". Is air dense? Or is lead dense?