Calculate $(a)$ wavenumber and $(b)$ frequency of yellow radiation having wavelength $5800 \, \mathring{A}$.

$(a)$ Calculation of wavenumber $(\bar{\nu})$:
$\lambda = 5800 \, \mathring{A} = 5800 \times 10^{-10} \, m = 5.8 \times 10^{-7} \, m$.
$\bar{\nu} = \frac{1}{\lambda} = \frac{1}{5.8 \times 10^{-7} \, m} \approx 1.724 \times 10^{6} \, m^{-1} = 1.724 \times 10^{4} \, cm^{-1}$.
$(b)$ Calculation of frequency $(\nu)$:
$\nu = \frac{c}{\lambda} = \frac{3 \times 10^{8} \, m \, s^{-1}}{5.8 \times 10^{-7} \, m} \approx 5.172 \times 10^{14} \, s^{-1}$.