What is the relationship between the wavelength of light absorbed and emitted by a fluorescent dye?

In fluorescence, a dye absorbs light energy at a specific wavelength, which excites its electrons to a higher energy state. After a short period, the dye returns to its ground state by emitting light. The key point here is that the energy of the absorbed light is usually greater than the energy of the emitted light, which corresponds to longer wavelengths.

Since the relationship between energy and wavelength follows the equation ( E = \frac{hc}{\lambda} ), where ( E ) is energy, ( h ) is Planck's constant, ( c ) is the speed of light, and ( \lambda ) is wavelength, this implies that a shorter wavelength corresponds to higher energy.

Therefore, when a fluorescent dye absorbs light, the wavelength of the absorbed light is indeed shorter than the wavelength of the light it emits. This results in a characteristic spectrum for the dye, with distinct peaks for absorption and emission, demonstrating the typical behavior of fluorescent materials. Hence, the correct answer reflects this fundamental principle of fluorescence.