Term Paper on Black Body Radiation Experiment | Quantum Physics | Physics

Here is a term paper on black body radiation experiment.

The wave theory of light was the dominant light theory in the 1800s. This theory was captured by Maxwell’s equations and surpassed Newton’s corpuscular theory. However the theory was challenged by how it explained thermal radiation, which is an electromagnetic radiation given off by objects based on their temperature. So how could someone test or detect thermal radiation?

Scientists can test for thermal radiation by setting up an apparatus to detect radiation from an object based on specific temperature, represented by T₁. Warm bodies give off radiation in all directions, so in order to be able to measure it effectively, shielding must be used so the radiation is examined in the form of a narrow beam.

In order to create this narrow beam, a scientist use a dispersive medium, such as a prism, placed between the body or object emitting the radiation and the radiation detector. This allows the radiation wavelengths to be dispersed at an angle. Then the detector measures a specific range or angle, essentially the narrow beam. This beam is considered a representation of the total intensity of the electromagnetic radiation across all the wavelengths. So let’s define a few key points. One thing to note is that the intensity per unit of a wavelength interval is referred to as radiancy.

Calculus notation helps us to reduce various values to zero and create the following equation:

dI = R(λ) dλ.

Using the prism, a scientist can detect dI, or the total intensity over all wavelengths, so one can define radiancy for any wavelength by working backwards through the equation. Now let’s look at how we can build a database of sorts for wavelength versus radiancy curves.

Scientists typically perform an experiment over and over again, building up a store of data that creates various ranges. When working with these ranges, one can begin to build a better understanding of how much radiation will occur from a specific object, but also how intense it will be at any given temperature.

For instances, one can glean that as the total intensity radiated increases as we increase or decrease the temperature. But when we look at the wavelength with the maximum radiancy, we find that the inverse occurs, that is with that specific wavelength, the intensity will go down as the temperature increases. Thus, as the temperature go up, wavelengths can change their individual radiation intensity, but the overall radiation intensity will continue to increase with the temperature.

So if the temperature is going to down, then the maximum intensity of an individual wavelength will go up, but the overall or total intensity of the object will go down, corresponding with the temperature.

Again, we go back to how to measure something when light reflects off so many things. How do you create the angle, making sure that you are accurately measuring your narrow beam?

A simple way to do this is to stop looking at the light and look at the object that doesn’t reflect it. Light does reflect off of objects, but scientists will perform this experiment observing a blackbody, or an object that doesn’t reflect any light at all.

Otherwise, the experiment runs into a difficulty defining what is being tested.

Performing this experiment requires a box, preferably metal, with a tiny hole. If or when light hits the hole, it enters the box but it won’t bounce back out. As a result, the hole, not the box, is the blackbody of the experiment. Any radiation detected outside of the hole is a radiation sample of the amount of radiation in the box. Scientists analyze this information to understand what’s happening within the box.

The first thing to be noted is that the metal box is being used to stop the electric field at each wall of the box, creating a node of electromagnetic energy at each of the walls. Thus standing electromagnetic waves are contained within the box.

Second, the number of standing waves with their various wavelengths within a defined range including an equation that takes into account the volume of the box. By analyzing the standing waves and then following this equation, it can be expanding into three dimensions.

Third, classical thermodynamics contributes a basic truth- the radiation in the box is in a thermal equilibrium with the walls of the box at a certain temperature. The radiation within the box is absorbed and reemitted from the walls constantly, creating oscillating within the radiation’s frequency.

The thermal kinetic energy of these oscillating atoms are simple harmonic oscillators, so the mean kinetic energy equals the mean potential energy. As a result, each wave contributes to the total energy of the radiation within the box.

Fourth, energy density is related to the radiance. Energy density is defined as the energy per unit volume within the relationship. The measurement of this is determined by the amount of radiation passing through a component of surface area with a cavity.

Classic physics as represented by the Rayleigh-Jeans formula failed to predict the actual results of these experiments, primarily due to the fact that classic physics failed to account for shorter wave lengths. At longer wavelengths, the Rayleigh- Jeans formula more closely matched the observed data. This failure was referred to as the ultraviolet catastrophe. In early 1900, this was a big issue, because it called into question such basic concepts as thermodynamics and electromagnetics as part of that equation.

Historically, this is where quantum physics came into play. Simply, Max Planck used quanta to create what would be defined as discrete bundles of energy. Thus the quanta would be proportional to the radiation frequency. With this theory, no standing wave could have more energy than kT, then high radiation frequency would be capped, solving the ultraviolet catastrophe. In the end, frequency describes the energy of each quanta, where a proportional constant.

While this resulted in an equation that fit the data of the experiments perfectly, but it wasn’t as attractive as the Rayleigh-Jeans formula. This formula became the starting point of quantum physics as we know it today. Einstein even demarcated it as a central principal of the electromagnetic field, while Planck had originally used it just to solve the issue of one experiment. While it took scientists a while to warm up to what is now known as Planck’s constant, it is now considered a critical part of the quantum physics or quantum mechanics.

This was just one part of the large array of experiments that define quantum physics. Another early experiment in concert with wave particle duality, a challenge that was known as the photoelectric effect.