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Unit of length is the Bohr radius:
$$
a_0 = {\hbar^2 \over { m_e e^2 } } 
\left( \ \ = 4 \pi \epsilon_0 {\hbar^2 \over { m_e e^2 } } \ \ \right)
$$
The first is in atomic units, second in SI-units. This quantity can be remembered
by recalling the  virial theorem, i.e. that in absolute value, half of the
potential energy is equal to the kinetic energy. This gives us
$$ 
{1 \over 2} {e^2 \over a_0 } =  {\hbar^2 \over { 2 m_e {a_0}^2 } }
$$
and if we accept this relation, we have the above value of $ a_0 $.


The so called fine structure constant
$$
\alpha = \frac{ e^2  } { \hbar c } 
$$
expresses in general the {\it weakness} of electromagnetic interaction.





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\centerline { \bf Some Constants and Quantities}
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$ v_0 = \alpha c = 2.187 10^{6}$ m s$^-1$  \ \ \ \ \ \ \ \ \ \  Bohr velocity

$ a_0 = 0.529177 \ 10^{-10}$ m  \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  Bohr radius 

$ \hbar = 0.6582 \ 10^{-15}$ eV s   \ \ \ \ \ \ \ \ \ \ \ \ Planck's constant

$k_{B} = 0.8625 \ 10^{-4}$ eV \char'27\hskip -0.2emK$^{-1}$  \ \ \ \ \ \ Boltzmann constant

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R = $N_{A} k_{B}$

$N_{A}  = 6.0222 \ 10^{23}$  \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Avogadro's number
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$\mu_{B} = 0.579 \ 10^{-4}$ eV (Tesla)$^{-1}$ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Bohr magneton
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\centerline { \bf Plank's formula}

$$
\rho(\omega_{ba}) \ = \ \frac{\hbar \omega^3_{ba} }{\pi^2 c^3 }
\ \frac{1} {e^{\hbar \omega/kT}-1} 
$$


%%%%Bohr magneton:

%%%%$\mu_{B} = 0.579 \ 10^{-5}$ eV (Tesla)$^{-1}$
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