Electron schwarzchild radius problem

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SUMMARY

The Schwarzschild radius of an electron is calculated to be 1.353 x 10^-57 meters. When applying the formula for the volume of a sphere, V = 4/3 * π * radius^3, the resulting volume at this radius is effectively zero due to arithmetic underflow, as the calculation yields a value less than 10^-99 cubic meters. This indicates a need for understanding operator precedence in calculations involving exponents. The discussion also references the concept of a black hole electron, suggesting further exploration of this topic.

PREREQUISITES
  • Understanding of Schwarzschild radius
  • Familiarity with basic geometry and volume calculations
  • Knowledge of operator precedence in mathematical expressions
  • Basic concepts of quantum mechanics
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  • Research the implications of the Schwarzschild radius in quantum mechanics
  • Learn about operator precedence in programming languages
  • Explore the concept of black hole electrons
  • Investigate the mathematical properties of extremely small volumes
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Physicists, mathematicians, students of quantum mechanics, and anyone interested in theoretical physics and the properties of subatomic particles.

mrllama
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The schwarszchild radius of an electron=1.353*10^-57m, and to work out the volume of a particle assuming it is spherical is 4/3*pi*radius^3 so the volume of an electron at its schwarzchild radius is 4/3*pi*1.353*10^-57^3 = 0??! WHAT DOES THIS MEAN :S
 
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I'd say it means you need to learn about operator precedence so that you don't confuse (10^-57)^3 with 10^-57^3 = 10^-185193, causing an arithmetic underflow on your calculator.
 
May I suggest it's because the volume in cubic meters in less than 10^-99, hence your calculator figures this is as good as zero. Fair enough wouldn't you say!
 
Anyways, applying the concept of Schwarzschild radius to an electron seems pointless.

EDIT: It appears it's not entirely pointless. There's even http://en.wikipedia.org/wiki/Black_hole_electron"
 
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