Bohrov model atoma (TEK U IZRADI! NE UPOTREBLJAVATI!)

$$\oint p_{\theta} d \theta = n \hbar$$ (1.68)

$$E = \frac {1}{2} m v^{2} - \frac {e^{2}}{r} = \frac {p^{2}_{\theta}}{2 mr^{2}} - \frac {e^{2}}{r}$$ (1.70)

$$\frac {m v^{2}}{r} = \frac {p^{2}_{\theta}}{m r^{3}} = \frac {e^{2}}{r^{2}}$$ (1.71)

$$\frac {e^{2}}{r} = \frac {p^{2}_{\theta}}{m r^{2}} = \frac {n^{2}\hbar^{2}}{mr^{2}} (\hbar \equiv \frac {\hbar}{2 \pi})$$ (1.72)

$$r_{n} = \frac {n^{2} \hbar^{2}}{m e^{2}}$$ (1.73)

$$E_{n} = - \frac {p^{2}_{\theta}}{2 mr^{2}} = - \frac {n^{2} \hbar^{2}}{2m} (\frac {me^{2}}{n^{2} \hbar^{2}})^{2}$$ (1.74)

$$= - \frac {R}{n^{2}}$$ (1.75)

$$R= \frac {m^{4}_{e}}{2 \hbar^{2}} = 2.18 \times 10^{-11} erg = 13.6 eV$$ (1.76)

$$r_{1} \equiv a_{0} \frac {\hbar^{2}}{me^{2}} = 5.29 \times 10^{-9} cm$$ (1.77)