Atomic Physics

Photon energy

E_{Photon} = \frac{hc}{\lambda} = hf = \hbar\omega

hf = W_{Out} + K = W_{Out} + eU_0

\lambda = \frac{h}{p} = \frac{h}{mv}

E_n = \left(\frac{h^2}{8mL^2}\right) \cdot n^2

\Psi_n(x) = \sqrt{\frac{2}{L}} \sin \left( n\frac{\pi x}{L} \right)

r = \frac{\epsilon_0h^2}{\pi \mu e^2}\frac{n^2}{Z}\approx a_0 \cdot \frac{n^2}{Z}

a_0=0.529 \; \textup{Å}

\frac{1}{\lambda} = R_M \cdot Z^2 \left( \frac{1}{n^2_1} - \frac{1}{n^2_2} \right)

R_M = \frac{e^4}{8 \varepsilon^2_0 h^3 c}\cdot \mu

\mu = \frac{m \cdot M}{m + M} \; \textup{Reduced mass}

R_M = R_\infty \cdot \frac{M}{M+m}

R_{\infty} = 109737.31568 \; \textup{cm}^{-1}

E_n = -Z^2 \frac{E_0}{n^2} \;\; \textup{where} \;\; E_0 = \frac{mk^2 e^4}{2 \hbar^2} = 13.6 \; \textup{eV}

L = \hbar \sqrt{l(l+1)}

|L| = \hbar\sqrt{l(l+1)}

\frac{m_p}{m_e} = 1836.152 673

\frac{1}{\lambda_{K_{\alpha}}} = \frac{3}{4}R_{\infty} \cdot (Z-1)^2

\frac{1}{\lambda_{L_{\alpha}}} = \frac{5}{36}R_{\infty} \cdot (Z-7.4)^2

\lambda_{min} = \frac{hc}{eU}

\mu = \frac{m_1 m_2}{m_1 + m_2}

I=\mu r^2

L = \mu r v = \mu r^2 \omega = I\omega

E_{rot} = \frac{l(l+1)\hbar^2}{2I}, \; I=\mu r^2

B = E_{0 r} = \frac{\hbar^2 }{2 I}

E_{vib} = \hbar \omega_0 \cdot (\nu + 1/2)

E_F = \frac{h^2}{8m}\left( \frac{3}{\pi}n\right)^{2/3}, \textup{where n is the electron density}

T_F = \frac{E_F}{k}

u_F = \sqrt{\frac{2 E_F}{m_e}}

n_e = f \cdot \frac{\rho \cdot N_A}{M}, \textup{where f is the number of free electrons per atom}

\rho = \frac{m_e v_{av}}{n_e e^2 \lambda}

\lambda = \frac{v t}{n_{ion} \pi r^2 v t} = \frac{1}{n_{ion} \pi r^2} = \frac{1}{n_{ion} A}

c_v = \frac{1}{2} \pi^2 \cdot R \cdot \frac{T}{T_F}