Urgent Modern Physics question

In summary, The conversation discusses the question of determining the width of an infinite quantum well in order to produce a photon of 450nm-wavelength during a lowest energy transition of an electron. The energy eigenvalue equation and the energy of a photon equation are given, and it is suggested to use them to solve the problem. A discrepancy in the equations is pointed out and additional help is offered. The correct answer is confirmed, but the person still struggles with finding the correct result due to a possible issue with the frequency.
  • #1
SuperCheetah
Here is a question that is giving me fits.

An electron is trapped in an infinite quantum well. If the lowest energy transition is to produce a photon of 450nm-wavelength, what should be the well's width?

Any help is appreciated. :)
 
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  • #2
The energy eigenvalue equation for an electron in a 1-D infinite square well is:

E(n) = (h^2 * n^2) / (8 * m * L^2),

where L is the width of the well.

A transition of energy states requires an emission or an absorption of a photon. The energy of a photon is:

E = h * f,

where f is the frequency of the photon.

Now you've got the equations; all you have to do is plug and chug.

eNtRopY
 
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  • #3
Nevermind got the frequency, my books equation says that there is a 2 on the bottom instead of an 8?
 
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  • #4
Call me an idiot but I'm still not getting the correct result. The answer is 0.064nm in width, but I keep getting extremely small numbers. Is there any additional help anyone might can give without totally giving away the problem? Thanks again!
 
  • #5
look closer at the 2 and 8 term, you will find that the difference is due to that h(bar)=h/(2*pi)

I´m not sure what you are doing with the equation, but you are looking for a difference, a delta E, dose that help?

Could you check you answer again, I´m getting an answer of ~ 6.4*10^(-10)?
 
  • #6
That is the correct answer you got, although I still wasn't able to get it before it was due. I can't figure out what I'm doing wrong. I'll try again later I guess. Thanks for the help. I think my problem lies in the frequency.
 

1. What is modern physics?

Modern physics is a branch of physics that deals with the study of the fundamental laws and properties of matter and energy at a microscopic level, including quantum mechanics and relativity.

2. What is the difference between classical and modern physics?

The main difference between classical and modern physics is the scale at which they operate. Classical physics deals with macroscopic objects and their motion, while modern physics focuses on the behavior of particles at the atomic and subatomic level.

3. How has modern physics changed our understanding of the universe?

The discoveries and theories of modern physics have greatly expanded our understanding of the universe. From the theory of relativity to quantum mechanics, modern physics has helped us understand the fundamental laws and behaviors that govern the universe at both the smallest and largest scales.

4. What are some practical applications of modern physics?

Modern physics has many practical applications, including the development of technology such as lasers, transistors, and nuclear power. It also plays a crucial role in fields such as medicine, telecommunications, and space exploration.

5. Is modern physics relevant to everyday life?

Yes, modern physics is relevant to everyday life in many ways. The principles of modern physics are used in technologies that we use every day, such as smartphones and GPS. It also helps us understand the natural phenomena that occur around us, from the behavior of light to the formation of stars and galaxies.

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