Bohr's Radius: Is His Calculation Right?

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In summary: Mosley's law is a mathematical relation that describes the energy levels of atoms in molecules. It is named after the British physicist Sir Cyril Mosley.In summary, the Bohr radius is a mathematical relation that describes the energy levels of atoms in molecules. It is named after the Danish physicist Niels Bohr, and it is almost correct for Helium. However, when it is applied to higher state of n, it fails miserably.
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I know that the Bohr theory is like "Santa Claus" in Physics, but is his way of calculating radius right? Because I've made some calculations for ground state of neutral Helium and singly ionized Lithium using the Bohr's radius. What I did for Helium was to take the energy level of singly ionized Helium (negative sign) add the Coulomb repulsive energy between 2 electron (because Helium neutral has 2 electrons) in the same shell of Bohr radius. I did almost a similar thing to singly ionized Lithium. The ground state energy I've got was surprisingly close to NIST database.
So can I say Bohr was right at least at the radius of the s-orbital?
 
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The Bohr radius is considered 'correct' for Hydrogen, in that his radius corresponds to the radius of maximal electron density in quantum theory (which inspired Bohr's 'theory of equivalence' between (semi-)classical and quantum results). The Bohr radius is also very nearly correct (using that definition) for Helium.
 
  • #3
Wow...this makes me so happy :D. I was surprised with such a random idea I've got. thank you ^^.
 
  • #4
I think the point is there is no "radius" at which the electron "orbits". The electron doesn't really make circular orbits around the nucleus, there is only a wavefunction. But the Bohr's radius does correspond to the maximum of the probability density in a Hydrogen atom as alxm suggests (though not the expectation value). (IIRC)
 
  • #5
yeah...base on my result, I would say that Bohr was right at least at the radius of the probability density in a Hydrogen atom, but for higher state of n, using the same approach, the Bohr radius failed miserably: adding the repulsion energy of 2 electrons to the Bohr's energy level, I got positive answer (when it supposed to be negative...). So I say electron in higher n does not travel in circular orbit, which mean the Bohr's assumption was wrong.
Does the Bohr radius have the same value with the maximum of the probability density in an excited atom, at least for the s orbital (the s because the wavefunction look kinda circular)? My guest is no, but I'm not that sure...
Thanks!
 
  • #6
MonsieurWise said:
I know that the Bohr theory is like "Santa Claus" in Physics, but is his way of calculating radius right? Because I've made some calculations for ground state of neutral Helium and singly ionized Lithium using the Bohr's radius. What I did for Helium was to take the energy level of singly ionized Helium (negative sign) add the Coulomb repulsive energy between 2 electron (because Helium neutral has 2 electrons) in the same shell of Bohr radius. I did almost a similar thing to singly ionized Lithium. The ground state energy I've got was surprisingly close to NIST database.
So can I say Bohr was right at least at the radius of the s-orbital?

For this type of calculation, Mosley's law may be of interest to you.
 
  • #7
Oh...thanks!
 

1. What is Bohr's Radius and why is it important?

Bohr's Radius is a measurement of the distance between the nucleus and the outermost electron in a hydrogen atom. It is important because it helps us understand the structure of atoms and their behavior.

2. How did Bohr calculate his radius?

Bohr used a combination of classical mechanics and quantum theory to derive his radius calculation. He based it on the assumption that electrons move in circular orbits around the nucleus, with the centripetal force balancing the electrostatic attraction between the two.

3. Is Bohr's calculation still considered accurate?

No, Bohr's calculation is not considered completely accurate as it does not take into account the effects of relativity and quantum mechanics. However, it is still used as a simplified model to understand atomic structure and is fairly accurate for simple systems like hydrogen.

4. How does Bohr's radius compare to the actual size of an atom?

Bohr's radius is much smaller than the actual size of an atom. The radius of an atom can vary depending on the element, but it is typically on the order of 0.1 nanometers, whereas Bohr's radius for hydrogen is about 0.05 nanometers.

5. Can Bohr's radius be applied to other elements besides hydrogen?

No, Bohr's radius is only applicable to hydrogen as it is a simplified model that does not take into account the different energy levels and electron configurations of other elements. Each element has its own unique radius calculation based on its number of protons, neutrons, and electrons.

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