# A spoonful of neutron star makes your spaceship explode

Note: This one has a “technical” tag, which means equations lay ahead!

I got a fun email today, and while it’s probably not quite right for my Ask a Physicist column, it’s actually a lot of fun to go through some of the numbers. A reader named Mark asked:

I know neutron star material is some of the most dense matter in the universe, with a teaspoon weighing as much as a mountain. My question is, If we could in fact extract this material from a neutron star, and reach escape velocity with a teaspoon of the material in cargo, (which is probably nigh impossible I understand) would the material remain in its super-dense state, decompress into some other form, or just become a cloud of neutrons? Would any type of energy be created in the decompression? I’m just curious as to what would happen if you were actually able to extract from its parent star.

Despite signing off with a “kthxbai”, I decided to answer him. A somewhat edited (mostly to include a few more explicit calculations) appears below:

Dear Mark,

Very bad things would happen to you.

For one thing what keeps a neutron star in its neutron star state is the critical pressure that comes from the gravity of a couple of solar masses. The neutrons keep the star from collapsing by something known as “degeneracy pressure,” which is really a fancy way of saying that the neutrons are packed together asses to elbows, and can’t be pushed any tighter. This also means, uncharacteristically for neutrons, that they can’t easily decay. Decay for a neutron means that an electron would be released and a neutron star is already far more compact (by about a factor of 1000) than electrons can be packed.

Let’s start with the simple question of how mass is in a teaspoon of a neutron star? A teaspoon is about 5ml, which has a volume of:

$5ml=5\times 10^{-6}m^3$

On the other hand, the density of a solar mass neutron star is about:

$\rho=\frac{M_\odot}{4\pi/3 (6km)^3}=2.2\times 10^{18}kg/m^3$

which means that our teaspoon has a mass of about:

$m=\rho V=1.1\times 10^{13}kg \simeq 10\ billion\ tons$

This is actually not a crazy mass for a mountain, give or take. The problem, though, is that once the neutrons aren’t confined by gravity, they’re free to decay into protons, electrons, antineutrinos, and a crapload of energy:

$n\rightarrow p+e^{-}+\overline{\nu}_e+\gamma$

How much energy? It’s all about

$E=mc^2$

Take the mass of the neutron and subtract the masses of the proton, the electron, and the negligible mass of the antineutrino, and that’s the mass lost. Multiply that by the speed of light squared, and you have the energy released. In the case of neutron decay, about 0.08% of the mass gets converted to energy in the process, which doesn’t sound like too much, but:

$E=1.1\times 10^{13}kg\times 0.0008 \times c^2\simeq 9\times 10^{26}J$

How much energy is that in real terms? This is the energy that would be released in a trillion megaton nuclear device. To put things in perspective, the device dropped on nagasaki, was 21 kilotons, a factor of 50 trillion less.

Bear in mind that the half-life of neutrons are about 10 minutes, which means everything would be dead and done quite quickly.

Best of luck to you.

Sincerely,

Dave

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### One Response to A spoonful of neutron star makes your spaceship explode

1. Elena says:

Dear Dave,
Thank You for the fabulous and simple explanation ! I really liked it!

And to add to Your words that “everything would be done quite quickly”…
maybe not! ðŸ™‚ if the neutrons are in fact intelligent…but before all they are pure Love… and no harm will be done, but whole Goodness! ðŸ™‚

All The Best!!!
Live Long and Prosper! ðŸ™‚