X-Ray photon/wavelength question

  • Thread starter Moomba44
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In summary, the conversation is about finding the wavelength of an X-ray photon with an energy of 7.90×10-16 J. The participants discuss using the equation E=hf to find the frequency and then using the formula v=fλ to calculate the wavelength. After some initial mistakes, the correct wavelength of 2.521x10^-9 m is determined.
  • #1
Moomba44
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This is one of the questions on my regular worksheets we have before our tests:

A fast-moving electron traveling through a vacuum tube slams into a piece of steel, coming abruptly to rest and emitting an X-ray photon with an energy of 7.90×10-16 J. What is the wavelength of the photon?

I know I have to find the frequency and speed of the photon in order to find the wavelength. The problem is I do not know how to find either of the two (I had a long day at work so I'm pretty sure I'm just having a brain fart right now). If someone could help point me in the right direction it would be more than appreciated!
 
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  • #2
Photons always travel at 3x10^8 m/s, the speed of light.
 
  • #3
For a photon:
[tex]E=hf[/tex]
[tex]E=[/tex]Energy of the photon
[tex]h=[/tex]Planck's Constant
[tex]f=[/tex]Frequency

and of course for any wave [tex]v=f \lambda[/tex], and like Pengwuin said in the case of photons your velocity is about 3x108 m/s
 
  • #4
Edit: Thank you dav, I thought I was on the right track but you confirmed it. Thanks a bunch guys!
 
  • #5
Okay, I think I had better post again, because something is surely off in what I am doing with this problem. My answer that I got for Frequency was something in the neighborhood of 1.16x10^-50 s, and whenever I plug that into the wavelength equation and solve for wavelength I get the astronomical number of 2.58x10^58 cm/s.

Am I doing this problem right and should be getting a number that high? Or am I off in some of my calculations?
 
  • #6
Look at the E=hf equation more carefully... I think you multiplied instead of divided.

Also keep in mind that wavelength has dimensions of length.
 
  • #7
to find f I've been putting in f = E/h, which I've been imputting as the energy from the original problem, 7.9 x 10^-16, divided by h, so it looks like 7.9 x 10^-16/6.626 x 10^-34. Is this wrong right here or is my calculator possibly giving me funky numbers for no reason? lol.
 
  • #8
[tex]\frac {7.9 \cdot 10^{-16}(J)}{6.626 \cdot 10^{-34}(J \cdot s)}[/tex] gives me a frequency of [tex]1.19 \cdot 10^{18} (\frac {1}{s})[/tex].
 
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  • #9
yeah, I realized i was putting something wrong into the equation, so for wavelength I got .252 cm...which corresponds to 2,520,000 nanometers...is this close to being right or am I still screwing something up?
 
  • #10
You divided 3x108m/s by 1.19x1018 1/s and got .00252 meters?

Check your calculations.
 
  • #11
Okay, I redid everything and I got 2.521x10^-9 m for the wavelength...I might as well take baby steps since either I or my calculator is screwing up what I type, so is this calculation correct? And if so, to convert it to nanometers I'm supposed to divide by 10^-9 if I'm not mistaken.
 

1. What is an X-ray photon?

An X-ray photon is a type of electromagnetic radiation with a very short wavelength, ranging from 0.01 to 10 nanometers. X-ray photons have high energy and can pass through many materials, making them useful in medical imaging and industrial applications.

2. How is the wavelength of an X-ray photon calculated?

The wavelength of an X-ray photon can be calculated using the equation λ = c/f, where λ is the wavelength, c is the speed of light (3 x 10^8 meters per second), and f is the frequency. X-ray photons have a high frequency, which results in a short wavelength.

3. What determines the energy of an X-ray photon?

The energy of an X-ray photon is determined by its frequency. The higher the frequency, the higher the energy. X-ray photons have a high frequency, which means they have a high energy level.

4. How are X-ray photons used in medical imaging?

In medical imaging, X-ray photons are directed at the body part being examined. The X-rays pass through the body and are absorbed by bones and other dense tissues, creating an image on a film or digital detector. This allows doctors to see inside the body and diagnose potential health issues.

5. What safety precautions should be taken when working with X-ray photons?

When working with X-ray photons, it is important to wear protective gear, such as lead aprons and gloves, to minimize exposure to radiation. Facilities that use X-rays also have safety protocols in place, such as limiting the amount of time someone is exposed to X-rays and ensuring equipment is properly maintained.

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