Question

In fluorescence, how does the energy of the emitted radiation compare with the energy of the exciting radiation?

Short answer

The energy of the emitted radiation in fluorescence is lower than that of the exciting radiation.

Step-by-step solution

Understanding Fluorescence

Fluorescence is a process where a substance absorbs light at one wavelength (exciting radiation) and then emits light at a longer wavelength. The energy of the emitted light is lower than that of the absorbed light because some energy is lost as heat or through non-radiative processes within the material.

Energy Relationship

In terms of energy, because wavelength and energy are inversely related (as per Planck's law, where energy is given by the equation \( E = h u \), with \( h \) being Planck's constant and \( u \) the frequency of light), the longer wavelength of the emitted light means it has lower energy compared to the exciting radiation.

Stokes Shift

The difference in energy between the absorbed and emitted light is known as the Stokes shift. This is a characteristic of fluorescent materials and is a clear indication that the emitted radiation is of lower energy than the exciting radiation.

Key concepts

Stokes Shift

In the fascinating world of fluorescence, Stokes shift plays a critical role in understanding the behavior of fluorescent materials. Stokes shift refers to the difference in energy – and therefore wavelength – between the absorbed light (excitation) and the emitted light (fluorescence).

When a molecule absorbs light, it momentarily reaches a higher energy state. As it relaxes back to a lower energy state, it emits light. However, the emitted light does not carry all the energy that was originally absorbed; some energy is dissipated as heat or through other non-radiative processes. Consequently, the emitted light has a longer wavelength and a lower energy. This phenomenon is precisely what is referred to as the Stokes shift.

The significance of the Stokes shift is manifold. It ensures that the emitted light can be distinguished from the exciting light, which is essential in applications like fluorescence microscopy or spectroscopy, where one needs to differentiate between different light sources.

Planck's Law

Delving into the core of fluorescence, it's impossible to ignore Planck's law, a cornerstone principle in the study of quantum mechanics. Planck's law reveals the relationship between the energy of a photon and its frequency: the energy (\( E \)) of a photon is equal to the frequency (\( u \)) of the light multiplied by Planck's constant (\( h \)), expressed in the equation \[ E = h u \.\]

Planck's constant is a fundamental value in physics that connects the world of the very small, such as atoms and photons, with the measurable phenomena we observe. In the context of fluorescence, Planck's law explains why the absorbed light, which has a higher frequency, also has more energy compared to the lower frequency of emitted light. This law is essential for students to grasp the underlying quantitative relationship that dictates the energy of photons and thus lays the foundation for understanding why fluorescence behaves the way it does.

Wavelength and Energy Relationship

Connecting the dots between wavelength and energy is imperative for students to visualize the energy transitions in fluorescent materials. The relationship is, simply put, inversely proportional. As the wavelength of the light increases, the energy of the photons decreases, and vice versa. This direct but inverse relationship is represented in the equation \[ E = \frac{hc}{\lambda} \.\]

Here, \( E \) is the energy, \( h \) is Planck's constant, \( c \) is the speed of light, and \( \lambda \) symbolizes the wavelength. This means that when a substance fluoresces, emitting light with a longer wavelength compared to the absorbed light, it is, in fact, emitting photons of lower energy.

Understanding this concept helps students to rationalize why the light seen from fluorescence is different in color and intensity from the light that has excited it. For example, when ultraviolet light (short wavelength, high energy) excites a substance, the visible light emitted (longer wavelength, lower energy) can appear as various colors, each representing a specific energy level according to the wavelength and energy relationship.