Sodium undergoes the photoelectric effect, with one electron absorbing a photon of violet light and another absorbing a photon of ultraviolet light. What is different about the two electrons afterward?

The photoelectric effect is a phenomenon where electrons are emitted from a material (in this case, sodium) when it absorbs energy from light (in this case, violet and ultraviolet light). Electrons absorb the energy from the photons, and if the energy is large enough, electrons are emitted from the material.

Energy (E) of a photon is related to its frequency (f) and wavelength (λ) through the following equation: E = h * f where h is the Planck's constant (6.63 x 10^{-34} Js). Similarly, we can relate frequency and wavelength by the equation: f = c / λ where c is the speed of light (3.00 x 10^8 m/s). By combining these two equations, we can determine the energy of absorbed light just by knowing its wavelength or frequency.

Violet light has a wavelength range of approximately 380-450 nm, while ultraviolet light falls in the range of 10-380 nm. As the wavelength decreases, the energy of the photon increases, making ultraviolet light higher in energy than violet light.

Since the ultraviolet photon has a higher energy than the violet photon, the electron that absorbs the ultraviolet photon will gain more energy than the electron that absorbs the violet photon. Therefore, this difference in energy after absorbing the photons will lead to different kinetic energies of the emitted electrons, which means the electron that absorbed the ultraviolet light will have a higher velocity after being emitted compared to the electron that absorbed the violet light. In conclusion, following the photoelectric effect, the electron that absorbed the ultraviolet light would have a higher velocity and kinetic energy than the electron that absorbed the violet light due to the higher energy content of the ultraviolet light.