Bohr Model

Bohr Model

1.

$$ \large \frac{m_e v^2}{r} = \frac{1}{4 \pi \epsilon_0} \frac{Z e^2}{r^2} $$

2.

$$ \large L = n \frac{h}{2 \pi} = n\hbar = mvr_n \quad \text{: angular momentum} $$$$ \large mv = \frac{n\hbar}{r_n} \quad \text{: linear momentum} $$

3.

$$ \large \Delta E = E_2 - E_1 = h \nu $$

Bohr Radius

$$ \large a_0 = \frac{4 \pi \epsilon_0 \hbar^2}{m_e e^2} $$

Bohr Energy

$$ \large E_n = - \frac{m_e e^4}{n^2 \hbar^2 2 (4 \pi \epsilon_0)^2} $$

Useful Properties

$$ \large \frac{E_\mu}{E_e} \propto \frac{\mu_\mu}{\mu_e} $$$$ \large \text{energy} \propto \text{reduced mass} $$

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