Would a Matchbox Full of Nuclei Weigh More Than the Earth?

I have heard a new amazing fact, that if we can fill a matchstick box with only nucleuses of atoms it would weight more than the weight of earth ? As we know that most of the mass of atom is concentrated in nucleus so how can a matchstick box full of nucleuses having much less nucleuses than the earth can weight more then earth ?
- Anshul (age 15)
UP, ghaziabad, INDIA

The density (mass/volume) of a nucleus is extremely high: about 2.3 × 10¹⁷ kg/m³ (according to ). That's about 100 trillion times more dense than liquid water, which is 1,000 kg/m³.

Let's say the dimensions of a matchbox are about 4 cm by 5 cm by 1.5 cm. Then the volume of a matchbox is about 30 cubic centimeters, or 3 × 10^-5 cubic meters. If we packed a matchbox full of material with nuclear density, its mass would be (3 × 10^-5 m³) × (2.3 × 10¹⁷ kg/m³) = 6.9 × 10¹² kg. That is really heavy--almost 7 billion metric tons. It's comparable to the mass of a neutron star, with a radius of a little less than a kilometer.

However, the mass of the earth is about 6 × 10²⁴ kg, which is still almost a trillion times more massive than the matchbox. So a typical matchbox stuffed with nuclei would be incredibly heavy, but not nearly as heavy as the earth.

This is still an amazing fact--and an interesting example of just how different the density of a nucleus is from the density of everyday objects. As you said, nearly all of the mass of an atom is concentrated in the nucleus, so most of the stuff around you is just "empty space." It's generally long-range forces between particles that make objects feel solid, not direct contact. In the nucleus, everything really is almost touching. It has to be that way, because the strong nuclear force that holds nuclei together against electrostatic repulsion between protons has a range of only about a femtometer, just a little larger than the radius of a proton.

A neutron star, formed when a massive star explodes in a supernova, is thought to have approximately the same density as a nucleus.

Rebecca Holmes

(published on 09/10/2014)