How Do Electron Wavelengths Compare in Different Transitions?

In summary, the question asks for the wavelength of a photon emitted from an electron transitioning from the third energy level to the lowest energy level in a box with a width of 0.1 nm. This can be calculated using the energy formula for the infinite-square well. Additionally, the wavelength associated with the transition from the third energy level to the ground state level in hydrogen can be found using the Bohr energy equation.
  • #1
shlomo127
9
0

Homework Statement


An electron makes a transition from the third energy level to the lowest energy level in a box of width 0.1 nm. what is the wavelength of the emitted photon? Compare this wavelength with the wavelength associated with the transition from the third energy level to the ground state level in hyrdogen. (The ground state energy of hydrogen is 13.6 eV. )


Homework Equations





The Attempt at a Solution


I am really lost. And this is one of the review questions for the test coming up.
Can anyone please get me started or at least point me in the right direction?
I would REALLY aprreciate it!
Thanks!
 
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  • #2
How is the energy of the nth level related to the width of the box?
 
  • #3
You should use the energy formula for the infinite-square well to obtain energy emitted, then I think you can use this energy in the formula of the photon and get the wavelength. Bohr energy equation can be used to find the energy for the hydrogen atom.
 

Related to How Do Electron Wavelengths Compare in Different Transitions?

1. What is an electron wavelength?

An electron wavelength refers to the distance between two consecutive peaks or troughs of a wave associated with an electron. It is a measure of the size of the electron's wave-like behavior and is related to its momentum and energy.

2. How do electron wavelengths compare to other wavelengths?

Electron wavelengths are much smaller than other types of wavelengths, such as those of light or sound. This is because electrons have much smaller masses and higher energies than photons or sound waves, resulting in shorter wavelengths.

3. What factors affect the electron wavelength?

The main factors that affect the electron wavelength are the energy and momentum of the electron. As the energy or momentum increases, the wavelength decreases. Additionally, the type of material the electron is traveling through can also affect its wavelength.

4. Why is comparing electron wavelengths important?

Comparing electron wavelengths allows scientists to better understand the behavior of electrons and their interactions with matter. This information is crucial in various fields, such as quantum mechanics, solid-state physics, and materials science.

5. How is electron wavelength measured?

Electron wavelength can be measured using various techniques, such as electron diffraction or electron microscopy. These methods involve directing a beam of electrons at a sample and analyzing the resulting diffraction pattern or image to determine the electron wavelength.

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