# Determine X-ray Wavelength & Frequency

• Von Neumann
In summary, the wavelength and frequency of the emitted x-rays when 100-keV electrons strike a target can be determined using the formula λ=hc/K and f=K/h, with the values of K=1.60x10^-14 J and hc=1240 eV-nm. The calculated values for λ and f are 0.12 Å and 2.4x10^19 Hz, respectively. It is important to double check for mistakes and ensure that the answer makes sense in relation to the problem.
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?

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.

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.

## 1. How is the wavelength of an X-ray determined?

The wavelength of an X-ray is determined by using a technique called X-ray diffraction. This involves passing X-rays through a crystal and measuring the angles at which the X-rays are diffracted. These angles can then be used to calculate the wavelength of the X-rays.

## 2. What is the relationship between wavelength and frequency for X-rays?

The relationship between wavelength and frequency for X-rays is inverse. This means that as the wavelength decreases, the frequency increases and vice versa. This relationship is described by the equation: c = λv, where c is the speed of light, λ is the wavelength, and v is the frequency.

## 3. How are X-rays produced?

X-rays are produced when high-energy electrons collide with a metal target. The energy from the collision is converted into X-rays, which are then emitted from the target. X-rays can also be produced through other methods, such as synchrotron radiation or X-ray tubes.

## 4. Can X-ray wavelength and frequency be controlled?

Yes, X-ray wavelength and frequency can be controlled by adjusting the energy of the electrons used to produce the X-rays. The higher the energy of the electrons, the shorter the wavelength and higher the frequency of the resulting X-rays. This allows for a wide range of wavelengths and frequencies to be produced for different applications.

## 5. What are some common uses of X-rays?

X-rays have a wide range of uses in various fields, including medicine, industry, and research. Some common uses of X-rays include medical imaging, material analysis, quality control in manufacturing, and studying the structure of molecules in chemistry and biology.

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