# How can we measure the wavelength of gamma-rays?

• B
How can we experimentally measure the wavelength of gamma-rays, say for about 0.7MeV?
Can it be done without gamma-ray spectrometry?

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Staff Emeritus
2019 Award
We don't measure wavelengths. We measure energies. If we want wavelength (and why?) we calculate it.

Astronuc
Staff Emeritus
How can we experimentally measure the wavelength of gamma-rays, say for about 0.7MeV?
Can it be done without gamma-ray spectrometry?
What wavelength does one calculate from the stated energy?

Bristol Instruments provides instruments to measure wavelength using interferometry, but the instruments are limited to light with wavelengths of 375 nm.
https://www.bristol-inst.com/bristol-instruments-products/wavelength-meters-scientific/

Otherwise, as V50 indicated we measure energy and calculate wavelength or frequency.

• vanhees71
hutchphd
I am confused by these answers. What then does Bragg diffraction of X-rays from a crystal measure?

mfb
Mentor
It gives direct wavelength measurements in the x-ray range, but I doubt this will give useful results at 700 keV.

Measuring the energy and calculating the wavelength will be better.

• vanhees71
hutchphd
Yes it certainly is easier. I am undecided as to whether that is actually a measurement of wavelength It is a measurement of energy from which wavelength may be inferred. This is largely a semantic point I guess (but not entirely so?) I guess all measurement requires a chain of inference.
As a practical matter it looks like the limit is indeed about 300keV photons for doing useful crystalline diffraction (this is my cursory literature search).

Astronuc
Staff Emeritus
I am confused by these answers. What then does Bragg diffraction of X-rays from a crystal measure?
I thought of Bragg diffraction, but 'measuring' the wavelength requires 'knowing' the distance between atoms in crystal. How does one 'know' or 'measure' the distance between atoms? X-ray diffraction.

Here is a paper that indicates "Measurement of X-ray spectral line wavelengths by using two Bragg reflections"
https://www.sciencedirect.com/science/article/abs/pii/0895399690900079

The term 'measuring' is important, in contrast to 'determining'. For example, we can measure distance or displacement, but we do not measure stress. Stress is calculated.

mfb
Mentor
How does one 'know' or 'measure' the distance between atoms? X-ray diffraction.
Or atomic force microscopy, these days. By far less precise than x-ray diffraction of course.
You can also measure it using interference with visible light (at large incidence angles), relating the x-ray wavelength to a measurement of visible light wavelengths that can be done with other methods.

Astronuc
Staff Emeritus
Or atomic force microscopy, . . .
I thought about AFM, but wasn't sure. I'm curious about the resolution. I could not find a definitive statement, other than noise on the order of 10s of pm. A 1 MeV gamma ray has a wavelength of ~1.24 pm (~0.00124 nm), so diffraction methods are too coarse. Atomic radii of most atoms are on the order of 100 pm, and lattice constants slightly larger.

Staff Emeritus
2019 Award
We're going far afield from the original question.

You can calibrate the x-ray wavelength from diffracation without being circular. You use x-ray diffraction to get the crystal structure - you don't need the spacing here, just the pattern. From the density and the atomic weight plus the crystal structure you get the atomic spacing. From the atomic spacing and the diffraction pattern you can get the wavelength.

• Astronuc, hutchphd and mfb
mfb
Mentor
I thought about AFM, but wasn't sure. I'm curious about the resolution. I could not find a definitive statement, other than noise on the order of 10s of pm. A 1 MeV gamma ray has a wavelength of ~1.24 pm (~0.00124 nm), so diffraction methods are too coarse. Atomic radii of most atoms are on the order of 100 pm, and lattice constants slightly larger.
You gain a lot from the angle. If you can determine the height of a layer to be e.g. 100 pm +- 3 pm your relative uncertainty on the wavelength from the lattice constant will just be 3%, even if you measure wavelengths below 10 pm because the diffraction angle is small. But, as V50 noted, you can also measure the mass of an atom and the mass of a macroscopic object.

• Astronuc