# Atomic numbers, and weights of objects

Do atomic numbers relate directly to weights of solid objects? As an example take these 3 elements, W, Au, and Pb,

74 W, Tungsten
79 Au, Gold

… if I had a chunk of Au that weighed 79 pounds, would the same size chunks of W and Pb weigh 74 and 81 pounds?

I ask because I now own two pieces of tungsten that were from my last job. They are unused parts of machinery, created to incorrect specifications, so basically they were discards. Each piece can be held in one hand, but they weigh about 40 lbs each. I’m fascinated by how deceptive their masses are.

I guess a related question is, are there any hazards by me keeping them? E.g., are they giving off minor radiation or something like that?

It wouldn’t if by “the same size chunks” you mean volume; it’s not only the atomic weight that differs between these three elements, but also their density. The rule does, however, work if by “the same size chunks” you mean amount of substance, in other words number of molecules or - in the case of pure elements, as we assume here - atoms. Amount of substance is measured in moles.

I did mean volume. Thanks for clarifying it for me.

Okay so then if I have the same volume of W, Au, and Pb, and if the W weighed 40 lbs, how much would the Au and Pb weigh?

Density is masse/volume
so 19,2 for tungsten, 19,3 for gold and 11,4 for lead…
so no relation.
As Schnitte says, if you were counting the same x quantity of atoms, their masses would be proportional to their atomic number.
The disproportion come from the fact that the atoms are not arranged in the same pattern : lead is face centered cubic, as gold whereas tungsten is body centered and atoms do not have the same diameter: 270 for tunsten and gold but 360 for lead.

Tungsten is generally inert and non-radioactive.

As Beowulf says, there have been some studies bonding leukemia with high concentration of tungsten in water, but if you don’t lick them, you’ll be fine.
Radioactivity is quasi non existent (only 180W is radioactive, but it form 0,12% of the metal and has a half life of 1,8 billion of billion years…)

What does that mean, 180W?

Tungsten-180, a particular isotope of Tungsten with a total of 180 nucleons (neutrons or protons). The number of protons is the identity of the element: tungsten always has 74 protons, but depending on isotope can have 106 or more neutrons. (180 is apparently the only naturally occurring radioisotope; the other 4 natural isotopes (182, 183, 184, and 186) are stable and radiologically inert)

“W” comes from Wolfram, the alternate name for Tungsten. @FrenchDunadan’s reference should have been marked up as 180W.

Nobody else has mentioned the OP’s confusion between atomic number and atomic mass? Atomic number is the number of protons in an atom, and is a constant for any given element: Gold, for instance, always has 79 protons in each atom. But atoms also contain neutrons, which weigh about as much as protons (and electrons, but they weigh much less than either), and so the total number of protons plus neutrons is what determines the atomic mass. Atomic mass usually increases with atomic number, but not always, and it doesn’t increase linearly, because while light elements usually tend to have the same number of protons and neutrons, heavy elements tend to have significantly more neutrons than protons. For instance, uranium, the highest-number element found in significant quantities in nature, always has 92 protons, but usually has 146 neutrons, for a total atomic mass of 238 (or sometimes 143 neutrons, or 142, or other numbers).

As for why densities aren’t just proportional to the masses of individual atoms, there are two factors at play: Different elements have the atoms arranged differently, and at different distances. Some elements, for instance, have atoms arranged in a square grid. But if you try to stack oranges or other round objects that way, you’ll find that they usually fall into a hexagonal sort of pattern (actually, one of two different hexagonal patterns), that fits more oranges into the same space, and some elements have atoms arranged that way, which makes them denser (other arrangements are also possible). And even with any given sort of arrangement, the spacing can vary from one element to another: Typically, inter-atom spacing is smaller as you get to the right side of the periodic table, and larger as you go down.

Carbon is an excellent example of crystal structure affecting density. Carbon as diamond (diamond lattice crystal) has a density of 3.52 gm/cm^2; carbon as graphite (hexagonal lattice) 2.25 gm/cm^2; and amorphous (non-crystalline) carbon 1.9 gm/cm^2. Same element, far different densities depending on how the atoms are arranged.

Yes, exactly. How do you do the little numbers?

<sup>whatever</sup> gives superscript
<sub>whatever</sub> gives subscript

To the original question, nope. Osmium and Iridium as bulk metals are denser than Uranium or Lead despite being having less massive nuclei. As others have said it’s partially how densely the atoms of that element will pack, and partially it’s that elements with more electron shells are bigger than atoms lower on the table of elements. Osmium and Iridium hit the sweet spot with regard to that.

Note though that for any given element, mass is proportional to atomic mass. If you had a chunk of isotopically pure 182W weighing 182 lbs, then an equal volume of 184W would weigh 184 lbs.

Technically, there would be a tiny nonlinearity due to the electrons, binding energy, etc., but this is relatively small.

Worth mentioning that alloys are even more perplexing. You can’t work out the density of an alloy by taking a weighted average of the constituent elements. The packing structure can be all over the place and the final density just plain unexpected.

True even for elemental metals. Tin for instance has two primary allotropes (distinct crystalline arrangements), alpha and beta. Alpha has a lower density than beta.