PX156 - B1 - atoms and atomic spectra

to determine the wavelength of light emitted/absorbed after an electron moves between energy levels, rydberg formula:

\frac{1}{λ} = R z^{2} (\frac{1}{m^{2}} + \frac{1}{n^{2}})

where, $m, n \in Z$ , $m < n$ ; $R = 1.097 \times 10^{7} m^{- 1}$ ; $z =$ atomic number

for hydrogen:
- $656.21, 436.07, 434.01, 410.12 n m :$ balmer series
$λ = 364.56 (\frac{n^{2}}{n^{2} - 4}) n m$
$n = 3 - 6$ for visible, $n = 7 - 9$ for UV
- $m = 1 :$ lyman (UV)
- $m = 2 :$ balmer (visible-UV)
- $m = 3 :$ paschen (IR)
for an emission:

h f = \frac{h c}{λ} = E_{i} - E_{f}

in $1913$ , niels bohr postulated a model that only a discrete set of possible states with energies is allowed, ie: $E_{n,} n \in Z$

\frac{1}{λ} = \frac{E_{i}}{h c} - \frac{E_{f}}{h c}

comparing with the rydberg formula:
- $\frac{E_{i}}{h c} = - \frac{R}{m^{2}} ⟹ E_{i} = R h c / m^{2}$
- $\frac{E_{f}}{h c} = - \frac{R}{n^{2}} ⟹ E_{f} = - R h c / n^{2}$
- energies are negative as electrons are bound