How Much Does 1ml of Protons Weigh?

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SUMMARY

The mass of 1 milliliter (ml) of protons, when hypothetically packed together, is approximately 1.7 x 10^12 kilograms. This calculation is based on the mass of a single proton, which is 1.6726231 x 10^-27 kg, and the assumption that 10^39 protons can fit into a cubic centimeter (the equivalent of 1 ml). The size of a proton is around 10^-15 meters, leading to the conclusion that a milliliter filled with protons would weigh about two trillion kilograms.

PREREQUISITES
  • Understanding of Avogadro's constant (approximately 6.0221415 × 10^23).
  • Knowledge of the mass of a proton (1.6726231 x 10^-27 kg).
  • Familiarity with the concept of volume in cubic centimeters (1 ml = 1 cm³).
  • Basic grasp of particle physics, specifically the size of subatomic particles (protons).
NEXT STEPS
  • Research the implications of packing protons in a given volume in particle physics.
  • Learn about Avogadro's law and its applications in chemistry.
  • Explore the concept of electrostatic forces between protons in close proximity.
  • Investigate the properties and behaviors of subatomic particles in quantum mechanics.
USEFUL FOR

Students in physics or chemistry, educators teaching particle physics, and anyone interested in the theoretical aspects of subatomic particle mass and volume calculations.

tish
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Can someone show me how to figure out the mass of 1ml. of protons?

I have been out of school for 20yrs. and have no clue as to how to do this.[
 
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ml stands for milliliter and that's a volume unit... Perhaps you mean mol?
In that case, 1 mol is a number of particles which equals Avagadro's constant, approx 6.0221415 × 10^23. The mass of a proton is 1.6726231 x 10^-27 kg.
 
If you do mean milliliter, and if we are talking about the fanciful notion of "if you could pack protons into a milliliter so that they "fill it up" and are all side by side...

Start with the size of the proton which is on at the order of a femptometer (10^-15 m). Since a mililiter is the same as a cubic centimeter, you could say a proton is 10^-13 cm across, therefore 10^13 protons lined up in a row would be 1 cm long.

Cube this number, and you have the number of protons that "fill up" a milliliter: 10^39 protons. Where did that electrostatic force go anyway?

So if each proton has a mass of 1.7 x 10^-27 kg, then the milliliter "full" of protons would have a mass of 1.7 x 10^12 kg. That's about two trillion kilograms.
 

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