Final answer:
Singlet and triplet excited states are distinguished by the spins of the electrons; singlet states have opposite paired spins, while triplet states have parallel unpaired spins. Photons are emitted when an electron transitions from an excited state to a lower state, and their energy can be calculated using ΔE = hν.
Step-by-step explanation:
The difference between a singlet excited state and a triplet excited state in an atom or molecule pertains to the spin states of the electrons involved. In a singlet state, the electron(s) have paired spins resulting in a total spin of 0, meaning the spins are opposite and cancel each other out. In contrast, a triplet state involves electrons with parallel spins, leading to a total spin of 1, indicating that they do not cancel each other out and hence, produce a magnetic field. The energies associated with these states differ due to the spin-spin interaction and the electromagnetic interaction with the magnetic field produced by the electron spins.
A photon is a quantum of electromagnetic radiation that is emitted when an electron transitions from a higher excited state to a lower energy state, such as the ground state. When considering sodium's spectral lines, the emitted photons correspond to the energies of the excited states the electron transitions from. The energy difference between the emitted photons when an electron falls from the first or second excited state to the ground state can be calculated using the equation ΔE = hν, where h is Planck's constant and ν (nu) is the frequency of the emitted photon. This equation relates the energy difference (ΔE) to the difference in frequency of the photons observed in the spectrum.