Which Formula Correctly Represents the Kinetic Orbital Momentum of an Electron?

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SUMMARY

The discussion centers on the correct formula for the kinetic orbital momentum of an electron in an atom. The two formulas presented are: a) L^2 = l(l+1)ħ/(4π^2) leading to L = ħ/(2π)√(l(l+1)), and b) L = nħ/(2π), where n represents the energy level of the electron. The first formula is derived from angular momentum theory in quantum mechanics, while the second is based on Bohr's postulates from his 1913 hydrogen atom model. The consensus indicates that the first formula is the accurate representation of kinetic orbital momentum.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with angular momentum in physics
  • Knowledge of Bohr's model of the hydrogen atom
  • Basic grasp of quantum numbers (l and n)
NEXT STEPS
  • Study the derivation of angular momentum in quantum mechanics
  • Explore the differences between classical and quantum mechanical models of atomic structure
  • Learn about quantum numbers and their significance in electron configurations
  • Investigate the historical context and implications of Bohr's postulates
USEFUL FOR

Students of physics, particularly those focusing on quantum mechanics, educators teaching atomic theory, and researchers exploring electron behavior in atomic structures.

C_Ovidiu
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In some places I saw that the module of the kinetic orbital momentum of an electron in an atom is
a) L^2=l(l+1)h^/(4pi^2) ==> L =h/(2pi)sqrt(l*(l+1)) l=0,1,2,...n-1
b) L=n*h/(2pi)
n beeing the energy level of an electron .

Now , my opinion is that the first is true . But I saw some problems solved using only the second value . I'm really confused . Which one is it ?
Thank you !
 
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Well, the first equation comes from the angular momentum theory in quantum mechanics, while the second is nothing but one of Bohr's postulates in his 1913 theory of the hydrogen atom.

Do you see what the difference is really about ?
 
Last edited:
Tks .
There are lots of differences .
 

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