Determine X-ray Wavelength & Frequency

[Von Neumann]

Problem:

Determine the wavelength and frequency of the emitted x-rays when 100-keV electrons strike a target.

Solution:

Assuming all kinetic energy of electrons is used to produce the x-rays,

E_initial=E_final
K+m_0*c^2=hf+m_0*c^2
K=hf
K=hc/λ
=>λ=hc/K=(6.63x10^-34 Js)(3.00x10^8 m/s)/(1.60x10^-14 J) [because 100 keV =1.60x10^-14 J]

λ=0.12 Å

Also since K=hf,

f=K/h=(1.60x10^-14 J)/(6.63x10^-34 Js)=2.4x10^-19 Hz

Is this correct?

 

[Redbelly98]

Looks essentially correct. Just recheck the exponent on your frequency (and my apologies if that's just a simple typo on your part)

I am wondering if this might have been intended as a "reverse photoelectric effect" problem. But since the work function is negligible compared to 100 keV, you come up with the same K≈hf to work with.

A few tips for working problems like this:

It goes easier if you can get used to working in eV rather than always converting to joules.

A useful constant to remember, for going between wavelength and photon energy, is hc=1240 \text{ eV-nm}

It's a good habit to think about whether your answer to any problem makes sense. For example, we (hopefully) know that visible light has a frequency way higher than 1 Hz, and x-rays have frequencies way higher than visible light. Again, my apologies if the 10^-19 was simply a typo.

 

[Von Neumann]

Oh yes, that is a typo! Should be x10^19~My apologies, but I'm happy you caught it.

Thanks for the tips, and I'll certainly put in time to commit the value for hc to memory.