Force of Gravity Between Proton & Electron in Hydrogen Atom

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SUMMARY

The force of gravity between a proton and an electron in a hydrogen atom is calculated using the equation F = G(m1 * m2) / r^2. Given the mass of a proton as approximately 1.67 x 10^-27 kg, the mass of an electron as approximately 9.1 x 10^-31 kg, and the distance between them as approximately 0.53 x 10^-10 m, the gravitational constant is 6.667300 x 10^-11 N-m^2/kg^2. The calculated gravitational force is approximately 3.61 x 10^-47 N, which has been confirmed as correct by community input.

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  • Understanding of Newton's Law of Universal Gravitation
  • Familiarity with scientific notation
  • Basic knowledge of atomic structure
  • Ability to perform calculations involving constants and variables
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  • Learn about quantum mechanics and its effects on atomic interactions
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Students of physics, researchers in atomic theory, and anyone interested in the fundamental forces governing atomic interactions will benefit from this discussion.

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I started pondering random thoughts earlier today and this was one of them; what is the force of gravity between a proton and electron in a hydrogen atom? Using the equation to find this force (F = G\frac{}m_{}1 * m_{}2{}r^{}2) I came up with my answer. However I wanted to ensure that my math was correct (and values for that matter) so I came here to ask.

Mass of a Proton ≈ 1.67 * 10^{}-27kg
Mass of an Electron ≈ 9.1 * 10^{}-31kg
Distance ≈ 0.53 * 10^{}-10m

Knowing that the gravitational constant is 6.667300 * 10^{}-11N-m^{}2/kg^{}2 I did the math and came up with ≈ 3.61 * 10^{}-47. Can someone confirm or deny this answer for me, and if it is wrong break down the math so I can get the correct values on my next calculation.

Thanks,
Taco
 
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