Bohr radius for single electron orbits

In summary, when dealing with ions with more than one proton, such as He+, Li2+, and Be3+, the extra charge does factor into the equation. This is because the elementary charge, denoted as e, needs to be replaced with Ze, where Z is the number of protons. This correction is often made in textbooks after initially deriving the equation with hydrogen in mind.
  • #1
xiankai
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for ions with more than one proton ie. He+, Li2+ and Be3+, doesn't the extra charge factor into the equation? because it seems only the elementary charge is http://en.wikipedia.org/wiki/Bohr_radius" , hence rendering it independent of amount of positive charge present.
 
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  • #2
xiankai said:
for ions with more than one proton ie. He+, Li2+ and Be3+, doesn't the extra charge factor into the equation?

Yes. For ions with a single electron but [itex]Z[/itex] protons, replace [itex]e[/itex] with [itex]Ze[/itex], where [itex]e[/itex] is the unit charge [itex]1.60 \times 10^{-19}[/itex] C.

Most textbooks do the derivation with hydrogen in mind, and later make the above correction for heavier, hydrogen-like ions.
 
  • #3
got it. thanks for the quick reply!
 

FAQ: Bohr radius for single electron orbits

1. What is the Bohr radius for single electron orbits?

The Bohr radius, denoted by a0, is a physical constant that represents the average distance between the nucleus and the electron in a hydrogen atom at its ground state.

2. How is the Bohr radius calculated?

The Bohr radius can be calculated using the formula a0 = ℏ² / (me * e2), where ℏ is the reduced Planck's constant, me is the mass of the electron, and e is the elementary charge.

3. What is the significance of the Bohr radius?

The Bohr radius is an important concept in atomic physics as it helps to determine the size and energy levels of atoms. It also provides a basis for understanding the stability of atoms and their electronic structure.

4. Does the Bohr radius vary for different atoms?

Yes, the Bohr radius varies for different atoms as it depends on the mass of the nucleus and the charge of the electron. For atoms with more protons in the nucleus, the Bohr radius will be smaller as the electrostatic force between the electron and the nucleus is stronger.

5. Can the Bohr radius be measured experimentally?

Yes, the Bohr radius can be measured experimentally using various techniques, such as spectroscopy and electron tunneling microscopy. These methods allow for the determination of the distance between the nucleus and the electron in different atoms and molecules.

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