For the Bohr radius rb = h^2 ε0 /π m e^2; take the centrifugal force equals the static electric attractive force in the atom. The ratio of any two of the above numbers is the fine structure constant α=e^2/ε0 hc; and what is notable is that this number is non dimensional, and the three electron radii are obtained in independent processes ...

Feb 12, 2023 · The bohr radius is derived by setting the centripetal force of electron to equal the coulomb force. $$\frac{mv^2}{r}=\frac{kq_1q_2}{r^2}.$$ The electron is not a particle orbiting the electron according to quantum mechanics. Its position is defined by its wave function. So, does the bohr radius make any sense quantum mechanically?

May 30, 2022 · According to Wikipedia, the Bohr radius (already described here) is:. a physical constant, approximately equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state.

Feb 23, 2015 · So the Bohr radius for a muonium atom is $\frac{1}{0.995} = 1.005$ times larger than a that of a hydrogen atom. But this, again, is the distance between the two particles rather than the size of the atom. So we multiply by $\frac{\mu}{m_e}$ again to get the distance of the electron to the barycenter of the system (as we did for positronium).

May 31, 2020 · $^\dagger$ The Bohr radius provides the characteristic length scale for the problem. If you wish, you could recall that ground state wavefunction is of the form $\psi(r,\theta,\phi)=c e^{-r/a}$ , and evaluate the expected value of $\frac{1}{r}$ ; if you do so, you will find $\langle \frac{1}{r}\rangle = \frac{1}{a}$ , justifying the inversion ...

Jun 19, 2020 · Even though the Bohr model might be replaced by more sophisticated models, the Bohr radius still lives on as one of the 4 fundamental constants in what is known as atomic units: It is very popular in software for atomic and molecular scale simulations.

Jun 1, 2023 · Muons, due to their higher mass, have a much smaller Bohr radius in an atom than electrons do. Muons have two spin states, just like electrons, so two muons can occupy the same orbital. A Be muonic atom with two muons will have a core with a helium-like structure, with two muons surrounding the nucleus.

May 15, 2023 · Ideally, we can solve Schrödinger's equation and may find a similar 1s wavefunction form, $$\psi_{1s, Yukawa} \sim e^{-\frac{r}{\alpha}}$$ where $\alpha$ is the 'Bohr radius analog' for this Yukawa Hydrogen atom.

Aug 6, 2020 · $\begingroup$ Since we know the Bohr model is false and there is no simple "radius" in real atoms, what do you mean by either of the relation being "correct" here? $\endgroup$ – ACuriousMind ♦ Commented Aug 6, 2020 at 14:52

Jan 15, 2022 · $\begingroup$ @watertruck Bohr radius is a natural unit made of the constants in the problem. It is ...