Question

The allowed energies of a quantum system are 0.0 eV, 6.0 eV , and 8.5 eV . What wavelengths appear in the system's emission spectrum? Enter your answers in ascending order separated by commas.

Answer 1

Emission refers the a decrease in the energy of the atom from a higher state to a lower state.

Case 1) An electron transits from 6.0 eV to 0.0 eV, thereby emitting a photon.

E = hc / ?

6 * 1.6 * 10^-19 = (6.63*10^-34)(3*10^8) / ?

? = 2.07 * 10^-7 = 207 nm

Case 2) An electron transits from 8.5 eV to 0.0 eV, thereby emitting a photon.

E = hc / ?

8.5 * 1.6 * 10^-19 = (6.63*10^-34)(3*10^8) / ?

? = 1.46 * 10^-7 = 146 nm

Case 3) An electron transits from 8.5 eV to 6.0 eV, thereby emitting a photon.

E = hc / ?

(8.5-6) * 1.6 * 10^-19 = (6.63*10^-34)(3*10^8) / ?

? = 4.97 * 10^-7 = 497 nm

Thus The wavelengths in ascending order are:

146nm, 207nm, 497nm

Use in m if needed in SI units.