The bright yellow light emitted by a sodium vapor lamp consists of two emission lines at \(589.0\) and \(589.6 \mathrm{~nm}\). What are the frequency and the energy of a photon of light at each of these wavelengths? What are the energies in \(\mathrm{kJ} / \mathrm{mol}\) ?

The frequencies and energies of the two emission lines at wavelengths \( 589.0 \mathrm{~nm} \) and \( 589.6 \mathrm{~nm} \) can be found using the formulas \( \nu = \frac{c}{\lambda} \) and \( E = h\cdot\nu \). After calculating the frequencies and energies, the energies can be converted to kJ/mol using the conversion factors \( 1 \mathrm{~J} = 1\times10^{-3} \mathrm{~kJ} \) and \( 1 \mathrm{~mol} = 6.022\times10^{23} \mathrm{~photons} \). The final results are: For \( 589.0 \mathrm{~nm} \) wavelength: frequency \( \nu_1 \), energy \( E_1 \), and energy in kJ/mol \( E_{1, kJ/mol} \). For \( 589.6 \mathrm{~nm} \) wavelength: frequency \( \nu_2 \), energy \( E_2 \), and energy in kJ/mol \( E_{2, kJ/mol} \).