Formula: Bohr Model Radius Velocity Principal quantum number
$$r_{\class{red}{n}} ~=~ \frac{\class{red}{n} \, \hbar}{ m_{\text e} \, v_{\class{red}{n}} }$$
$$r_{\class{red}{n}} ~=~ \frac{\class{red}{n} \, \hbar}{ m_{\text e} \, v_{\class{red}{n}} }$$
$$v_{\class{red}{n}} ~=~ \frac{\class{red}{n} \, \hbar}{ m_{\text e} \, r_{\class{red}{n}} }$$
$$\class{red}{n} ~=~ \frac{m_{\text e} \, r_{\class{red}{n}} \, v_{\class{red}{n}} }{ \hbar }$$
Radius
$$ r_{\class{red}{n}} $$ Unit $$ \mathrm{m} $$
The quantized radius of the orbit of an electron in the \(\class{red}{n}\)-th state in the framework of the Bohr model.
Velocity
$$ v_{\class{red}{n}} $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$
The quantized velocity of the electron in the \(\class{red}{n}\)-th state in the framework of the Bohr model.
Principal quantum number
$$ \class{red}{n} $$ Unit $$ - $$
The principal quantum number \( \class{red}{n} = 1, 2, 3, ...\) numbers the discrete energy states of an electron in the atom.
Reduced Planck's constant
$$ \hbar $$ Unit $$ \mathrm{Js} = \frac{ \mathrm{kg} \, \mathrm{m}^2 }{ \mathrm{s} } $$
Reduced Planck's constant is a physical constant (of quantum mechanics) and has the value: \( \hbar ~=~ \frac{h}{2\pi} ~=~ 1.054 \,\cdot\, 10^{-34} \, \text{Js} \).
Electron mass
$$ m_{\text e} $$ Unit $$ \mathrm{kg} $$
The rest mass of an electron is a physical constant with the value:
$$ m_{\text e} ~=~ 9.1 ~\cdot~ 10^{-32} \, \mathrm{kg} $$