Final answer:
The wavenumber value of the green light associated with the aurora borealis is 0.0179 cm^-1. The energy of a photon emitted by an excited oxygen atom is 1.121 x 10^-19 J. The energy in kilojoules of a mole of such photons is 6.7444 x 10^4 kJ/mol.
Step-by-step explanation:
(a) The wavenumber value can be calculated using the formula:
Wavenumber (cm-1) = 1 / Wavelength (cm)
Since the wavelength of the green light is 557.7 nm, we need to convert it to cm by dividing it by 10:
Wavelength (cm) = 557.7 nm / 10 = 55.77 cm
Now we can calculate the wavenumber:
Wavenumber (cm-1) = 1 / 55.77 cm = 0.0179 cm-1
(b) The energy of a photon can be calculated using the formula:
Energy (J) = Planck's constant (6.626 x 10-34 J·s) x Speed of light (3.00 x 108 m/s) / Wavelength (m)
First, we need to convert the wavelength from nm to m by dividing it by 109:
Wavelength (m) = 557.7 nm / 109 = 5.577 x 10-7 m
Now we can calculate the energy:
Energy (J) = (6.626 x 10-34 J·s) x (3.00 x 108 m/s) / (5.577 x 10-7 m) = 1.121 x 10-19 J
(c) To determine the energy in kilojoules of a mole of such photons, we need to multiply the energy of one photon by Avogadro's number (6.022 x 1023 mol-1):
Energy (kJ/mol) = (1.121 x 10-19 J) x (6.022 x 1023 mol-1) / 1000 = 6.7444 x 104 kJ/mol