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The Bohr radius, central to atomic physics and quantum mechanics, is the radius of the smallest orbit in the Bohr model of the atom, specifically the hydrogen atom. It is also applicable to other hydrogen-like atoms. This tutorial explains the formula for the Bohr radius, the creators of the formula, its real-life applications, key contributors, and interesting facts about this cornerstone concept.

Bohr Radius = |

The formula for the Bohr radius (a_{0}) is:

a_{0} = 4πε_{0}ℏ^{2} / (m_{e}e^{2})

Where:

**a**: Bohr radius_{0}**ε**: The permittivity of free space (a physical constant)._{0}**ℏ**: Reduced Planck's constant, defined as Planck's constant divided by 2π.**m**: The electron rest mass._{e}**e**: The elementary charge, which is the charge of an electron.

The formula was first introduced by Niels Bohr in 1913 as part of his Bohr model of the atom. The Bohr radius has relevance in various fields beyond atomic physics and quantum mechanics, including condensed matter physics, molecular physics, and even in certain aspects of chemistry, especially quantum chemistry.

The Bohr radius is used extensively in the study and application of spectroscopy, a technique used for the identification of substances through the spectrum emitted from or absorbed by them. Spectroscopy, particularly atomic spectroscopy, uses the Bohr model and the associated Bohr radius to predict the wavelengths of light that a hydrogen-like atom can absorb and emit.

The primary individual associated with the Bohr radius is Niels Bohr, a Danish physicist who proposed the Bohr model of the atom. His contributions to the field of atomic structure and quantum theory were recognized with the Nobel Prize in Physics in 1922.

- The Bohr radius is named in honor of Niels Bohr, who introduced the concept. Its value is approximately 5.29177210903(80) × 10
^{-11}m, a size that is nearly impossible to comprehend at the human scale. - The Bohr model and the Bohr radius, despite their simplicity, provide a surprisingly accurate description of the hydrogen atom, which is one of the reasons why these concepts are fundamental in quantum physics.
- These ideas have influenced numerous developments in physics and other fields. For instance, they underpin the quantum mechanical models of more complex atoms and the understanding of chemical bonding.

The Bohr radius is a key concept in understanding atomic structures, particularly hydrogen-like atoms. Despite its simple derivation from the Bohr model of the atom, it has far-reaching implications in several fields of science and has played a significant role in advancing our understanding of the atomic world.

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