I love his “What If?” even more than his cartoons. Yesterday I was wondering if he could tell me what would happen if all of the electrons in my body instantly vanished. Specifically how big the explosion would be but also whether a bunch of free protons and nuclei at that energy level would do anything exciting.
In your body there are about 0.55 electrons for each nucleon (from this and approximating Z/A as 1 for hydrogen and 0.5 for anything else); i.e., about 3.3e26 electrons per kilogram of matter; that is, their electric charge is about −5.3e7 coulombs per kilogram, and the electric charge of your body if the electrons vanished would be 5.3e7 C/kg. The electrostatic energy is then kQ^2/(4*pi*ε0*r), where r is your “size” and k is some factor roughly of order 1 depending on your “shape” (e.g. 3⁄5 for an uniform ball of radius r). That’d be in the ballpark of 1e30 joules, or 1e14 megatons of TNT: half a dozen orders of magnitude more than the Chicxulub Crater, but about fourteen orders of magnitude less than a supernova.
That’d be in the ballpark of 1e30 joules, or 1e14 megatons of TNT: half a dozen orders of magnitude more than the Chicxulub Crater, but about fourteen orders of magnitude less than a supernova.
So from the sounds of it extinction of complex life on earth but nowhere near enough to destroy the planet.
After estimating the total energy and thence the energy per particle, it looks like the average particle would have UHECR-like energy, so they would each generate an extensive air shower, “spreading” the energy over larger volumes than it otherwise would. (But when you have so many showers superimposed to each other, I’m not sure the total effect would be much different from each particle interacting locally.)
This looks like a job for Randall!
I love his “What If?” even more than his cartoons. Yesterday I was wondering if he could tell me what would happen if all of the electrons in my body instantly vanished. Specifically how big the explosion would be but also whether a bunch of free protons and nuclei at that energy level would do anything exciting.
In your body there are about 0.55 electrons for each nucleon (from this and approximating Z/A as 1 for hydrogen and 0.5 for anything else); i.e., about 3.3e26 electrons per kilogram of matter; that is, their electric charge is about −5.3e7 coulombs per kilogram, and the electric charge of your body if the electrons vanished would be 5.3e7 C/kg. The electrostatic energy is then kQ^2/(4*pi*ε0*r), where r is your “size” and k is some factor roughly of order 1 depending on your “shape” (e.g. 3⁄5 for an uniform ball of radius r). That’d be in the ballpark of 1e30 joules, or 1e14 megatons of TNT: half a dozen orders of magnitude more than the Chicxulub Crater, but about fourteen orders of magnitude less than a supernova.
So from the sounds of it extinction of complex life on earth but nowhere near enough to destroy the planet.
Prob’ly something like this.
Ahh, good point. That seems about right.
After estimating the total energy and thence the energy per particle, it looks like the average particle would have UHECR-like energy, so they would each generate an extensive air shower, “spreading” the energy over larger volumes than it otherwise would. (But when you have so many showers superimposed to each other, I’m not sure the total effect would be much different from each particle interacting locally.)