Transition energy in quantum dots

In summary, the conversation discusses the dependence of transition energy on the number of molecules in a quantum dot. The equation E∝1/N^2/3 is used to describe this relationship, and the conversation explores the concept of quantum energy and how it relates to the number of molecules in the dot. The conversation also mentions the use of fractals and simplifying calculations to understand this concept.
  • #1
liran avraham
7
0

1. Homework Statement

show that tthe transition energy can depend on the number of molecules in the quantum dot according to:
E∝1/N^2/3

in a intro course to nanotechnology class the prof gave us this question and said that "its very easy"
but i wasnt able to prove this.
can someone give me some guidance/insight?
i thought that the fractal is maybe an error and asked him but he said that its not.
 
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  • #2
Well, "quantum" means energy is associated with frequency and hence wavelength. How would the number of molecules affect this?
 
  • #3
The fractal is correct and this is indeed one (a pretty oversimplifying one) of the very basic calculations to get people started.

First, consider the quantum dot as a one-dimensional particle in a box problem with infinite barriers. How does the energy of the ground state of this system scale with the width of the box?

Next, you consider the quantum dot as such a box. Consider it as a large sphere (the QD) made out of several small spheres (the molecules) The inside of the large sphere is the box. How does the radius of the large sphere depend on the number of molecules? Then put both results together.
 

1. What is transition energy in quantum dots?

Transition energy in quantum dots refers to the energy needed for an electron to move from one energy level to another within the quantum dot. This energy is typically in the form of photons, which are absorbed or emitted by the electrons during the transition.

2. How is transition energy related to the size of quantum dots?

The size of quantum dots directly affects the transition energy. As the size of the quantum dot decreases, the energy difference between the electron's energy levels increases, resulting in a higher transition energy. This is because the smaller size of the quantum dot leads to a stronger confinement of the electron, making it harder for the electron to move between energy levels.

3. What factors influence the transition energy in quantum dots?

The transition energy in quantum dots is influenced by several factors including the size and shape of the quantum dot, the type and number of atoms present in the dot, and the surrounding environment. Additionally, the material used to create the quantum dot and the method of fabrication can also impact the transition energy.

4. How is transition energy measured in quantum dots?

Transition energy in quantum dots is typically measured using spectroscopy techniques, such as absorption or photoluminescence spectroscopy. These techniques involve shining light onto the quantum dot and measuring the wavelengths of light that are absorbed or emitted, which can then be used to calculate the transition energy.

5. What are the potential applications of transition energy in quantum dots?

Transition energy in quantum dots has many potential applications, including in optoelectronic devices such as solar cells, LEDs, and lasers. By controlling the transition energy, scientists can tune the properties of quantum dots to be more efficient and versatile in these applications. Additionally, transition energy can also be used in quantum computing and as a tool for studying the behavior of electrons in confined systems.

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