Question

Question: Incandescent lightbulbs heat up a filament “white hot,” producing light of all wavelengths that has little to do with the filament’s composition. Gas vapor bulbs, such as sodium and mercury streetlights, produce colors that do depend on the gas in the bulb. Viewed with a diffraction grating (even a simple CD!), whereas the incandescent spectrum is continuous, that of a gas vapor (or fluorescent) bulb has characteristic lines. How is this indirect evidence of the wave nature of orbiting electrons?

Short answer

Answer:

Only specific quantized energies are allowed for orbiting electrons, which leads to only specific wavelengths of photons. The electron should act like a wave inside the tiny constraints of the atom, creating quantized standing waves.

Step-by-step solution

The wavelength of a particle 

The wavelength of a particle can be obtained using the formula $\mathit{\lambda }\mathbf{=}\frac{\mathbf{h}}{\mathbf{p}}\mathbf{=}\frac{\mathbf{h}}{\mathbf{m}\mathbf{v}}$.

Explanation

Gas vapor filaments, like sodium, form distinctive lines, or lines with particular wavelengths or energy. This indicates that, in accordance with the energy conservation principle, electrons either make the same transition across energy levels or exist in quantized states.

Bohr offered the theory that electrons behave as a wave that is contained in an orbit around the nucleus as one explanation. In accordance with this, some wavelengths (standing waves) can fit within these circles, much as how sound waves can fit inside of closed pipes or other musical instruments.