Question

A blackbody is an ideal system that a) absorbs \(100 \%\) of the light incident upon it, but cannot emit light of its own. b) emits \(100 \%\) of the light it generates, but cannot absorb radiation of its own. c) either absorbs \(100 \%\) of the light incident upon it, or emits \(100 \%\) of the radiation it generates. d) absorbs \(50 \%\) of the light incident upon it, and emits \(50 \%\) of the radiation it generates. e) blackens completely any body that comes in contact with it

Short answer

Answer: The properties of a blackbody include both absorbing 100% of the light incident upon it and emitting 100% of the radiation it generates.

Step-by-step solution

Definition of a Blackbody

A blackbody is an idealized system that absorbs 100% of the electromagnetic radiation incident upon it and emits radiation according to its temperature. This means it can both absorb and emit radiation, and its emitted spectrum depends on its temperature. Now let's analyze each option to identify the correct one.

Option a)

This option suggests that a blackbody absorbs 100% of the light incident upon it but cannot emit light. This is incorrect as a blackbody also emits radiation according to its temperature.

Option b)

This option suggests that a blackbody emits 100% of the light it generates but cannot absorb radiation. This is incorrect as a blackbody also absorbs 100% of the radiation incident upon it.

Option c)

This option suggests that a blackbody either absorbs 100% of the light incident upon it or emits 100% of the radiation it generates. This is the correct definition as it accounts for both absorption and emission characteristics of a blackbody.

Option d)

This option suggests that a blackbody absorbs only 50% of the light incident upon it and emits 50% of the radiation it generates. This is incorrect as a blackbody absorbs 100% of the incident radiation and emits radiation according to its temperature.

Option e)

This option suggests that a blackbody blackens completely any body that comes in contact with it. This is incorrect as blackening of objects has nothing to do with the blackbody properties related to radiation absorption and emission. Therefore, based on our analysis, the correct answer is:

Conclusion

The properties of a blackbody include both absorbing 100% of the light incident upon it and emitting 100% of the radiation it generates. So the answer is: c) either absorbs 100% of the light incident upon it, or emits 100% of the radiation it generates.

Key concepts

Absorption of Radiation

A fundamental characteristic of a blackbody is its ability to absorb all the radiation that strikes it. This phenomenon is known as the absorption of radiation. Unlike most materials, which reflect or transmit a portion of incoming light, a blackbody captures every bit of it. This means it absorbs light of all wavelengths and does not reflect any, appearing perfectly black, hence the name "blackbody."

The concept of a blackbody is crucial in physics because it serves as a baseline to understand how real objects interact with radiation. When radiation hits a blackbody, it doesn't bounce back or pass through; instead, it is completely absorbed and contributes to the energy of the system. This absorbed energy then plays a role in determining the temperature of the blackbody and the subsequent emission of radiation.

Understanding this behavior is vital in studying radiative balance, heat transfer, and thermal radiation across various scientific and engineering fields.

Emission of Radiation

Just as a blackbody perfectly absorbs all incident radiation, it also emits radiation effectively. The emission of radiation by a blackbody depends entirely on its temperature. This relationship is described by Planck's law, indicating that the wavelength composition of emitted radiation shifts with temperature.

At cooler temperatures, a blackbody emits mostly in the infrared spectrum, which is invisible to the human eye. As the temperature increases, the peak of emission moves to shorter wavelengths, eventually entering the visible spectrum. This is why a heated metal, like from a stove or a lava flow, begins to glow red and then white-hot as temperature escalates.

The rate at which a blackbody emits radiation is given by the Stefan-Boltzmann law. It states that the power emitted per unit area is proportional to the fourth power of the blackbody’s absolute temperature: \[ E = \sigma T^4 \]where \( E \) is the emissive power, \( \sigma \) is the Stefan-Boltzmann constant, and \( T \) is the temperature in Kelvin. This principle helps scientists understand energy transfer and electromagnetic radiation in natural and artificial contexts.

Idealized System

A blackbody is often used as an idealized system in theoretical models to simplify the complex interactions between radiation and matter. Because it absorbs and emits radiation perfectly, it provides a convenient reference point for comparing real-world materials and systems.

In many scientific applications, it's crucial to have a theoretical model to make observations and predictions. An idealized system like a blackbody allows researchers to strip away real-world complexities and focus on fundamental principles. This idealization is pivotal in developing laws related to radiation, energy transfer, and thermodynamic equilibrium.

Moreover, the study of blackbody radiation paved the way for quantum mechanics and the understanding of atomic and molecular energy levels. While no material perfectly matches the properties of a blackbody in nature, understanding this theoretical model enables advancements in technologies such as thermal imaging, climate modeling, and astrophysical observations.