Final answer:
The energy levels of the hydrogen atom relate to its spectrum as electrons move between these quantized levels, absorbing or emitting photons with energies equivalent to the difference between these levels. This results in the hydrogen spectrum's characteristic line emissions, which are observable when hydrogen gas is heated.
Step-by-step explanation:
The energy levels in the hydrogen atom are integral to understanding its emission spectrum. According to the Bohr model, the energy of an electron in a hydrogen atom is quantized and can only take on certain discrete values, calculated with the formula 13.6 eV / n² where n is the principal quantum number corresponding to different energy levels. For n = 1, which is the ground state, the energy level is -13.6 eV. For higher energy levels, the values can be calculated as:
- n = 2: -3.4 eV
- n = 3: -1.51 eV
- n = 4: -0.85 eV
- n = 5: -0.54 eV
- n = 6: -0.38 eV
Transitions between these energy levels result in the emission or absorption of photons with specific wavelengths, explaining the characteristic line spectrum of hydrogen. When an electron jumps to a higher energy level, it absorbs a photon with energy equal to the difference between the two levels. Conversely, when it drops to a lower energy level, it emits a photon with the corresponding energy difference.
The reason hydrogen emits light at certain wavelengths when heated is because the electrons transition between energy states, emitting light at specific colors. The correct explanation is (b): As the gas heats up, the electrons within the hydrogen atoms are excited to high energy levels. As the electrons transition to lower energies, they emit light of specific colors, giving the spectrum its lien appearance.