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The \(\textit{Bohr Radius}\) is a physical constant, approximately equal to the most probable distance
between the proton and electron in a hydrogen atom in its ground state.
It is named after Niels Bohr, due to its role in the Bohr model of an atom.
The precise definition of the Bohr radius is:
\[a_0 = \frac{4\pi \epsilon_0 \hbar^2}{me^2}\]
Where,
\(a_0\) is the Bohr radius,
\(\epsilon_0\) is the permittivity of a vacuum,
\(m_e\) is the mass of an electron,
\(\hbar\) is the reduced Planck's constant,
\(e\) is the elementary charge.
When rearranged to highlight the role of the Coulomb constant and the elementary charge,
the formula can be shown as:
\[a_0 \equiv \frac{{\hbar ^2 }}{{m_e ke^2 }}\]
Where,
\(a_0\) is the Bohr radius,
\(m_e\) is the mass of an electron,
\(\hbar\) is the reduced Planck's constant,
\(k\) is the Coulomb Constant,
\(e\) is the elementary charge.
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