X-Ray photon/wavelength question

[Moomba44]

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!

 

[Pengwuino]

Photons always travel at 3x10^8 m/s, the speed of light.

 

[dav2008]

For a photon:
$$E=hf$$
$$E=$$Energy of the photon
$$h=$$Planck's Constant
$$f=$$Frequency

and of course for any wave $$v=f \lambda$$, and like Pengwuin said in the case of photons your velocity is about 3x10⁸ m/s

 

[Moomba44]

Edit: Thank you dav, I thought I was on the right track but you confirmed it. Thanks a bunch guys!

 

[Moomba44]

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?

 

[dav2008]

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.

 

[Moomba44]

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.

 

[dav2008]

$$\frac {7.9 \cdot 10^{-16}(J)}{6.626 \cdot 10^{-34}(J \cdot s)}$$ gives me a frequency of $$1.19 \cdot 10^{18} (\frac {1}{s})$$.

 

[Moomba44]

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?

 

[dav2008]

You divided 3x10⁸m/s by 1.19x10¹⁸ 1/s and got .00252 meters?

Check your calculations.

 

[Moomba44]

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.