# Something weird with my Kurie-Plot (Beta Spectroscopy)

• virtuosowanaB
In summary, the speaker is conducting a Beta Spectroscopy of Sodium and is using the Kurie Plot to incorporate the Coulomb Correction Factor F(Z,p). However, when plotting the data, the K(Z,p) value is extremely large, on the order of 1020, and the linear graph appears distorted. The speaker explains their steps and equations used in the calculation, including the use of standard constants and the daughter nucleus of the decay being Ne with Z=10. They also provide a link to their spreadsheet containing the Kurie Plot Data and Energy Spectrum Data. The speaker mentions trying to plot sqrt(N/B^3) as an alternative, but the resulting linear graph is also distorted. They question if they are overlooking something and mention

#### virtuosowanaB

So I'm doing a Beta Spectroscopy of Sodium and apart from the Energy Spectrum, I'm intending to use the Kurie Plot to incorporate the Coulomb Correction Factor F(Z,p). But when I try plotting the data, my K(Z,p) has an incredibly huge number, on the order of 1020 and the linear graph looks weird. My Count Rate vs Energy selected graph is alright.

Here are my steps.

I am using the equation

- K(Z,p) = √{ N(p)/(p2F(z,p))}

- F(Z,p), I'm using = {2πη}/{ 1 - e(-22πη)}

where η = (Zq2)/( ħv)

- To calculate v, I'm using v = BqR/m

- So to calculate p2 I'm using (mv)2 = (BqR)2

- Daughter nucleus of the decay is Ne. Z = 10.

- For N(p), I'm using the number of counts measured over an interval of
4 minutes.

The rest are pretty much standard constants.

So for each corresponding count, there would be a corresponding energy selected.

And I will plot the K(Z,p) on the y-axis, vs Energy (keV) on the x-axis.

Is there anything wrong that I'm doing with my Kurie Variable calculation?

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You might want to show a data point and your calculations including all units being carried through. There's nothing obviously wrong with what you've explained so far, but I will note that the electric charge in SI units is ##1.6\cdot 10^{-19}##~C, which might explain the overall scaling problem you claim to have.

It has my Kurie Plot Data, as well as my Energy Spectrum Data.
My adjusted R-squared value for the Energy Spectrum is 0.99, which I believe has a decent accuracy.

I also read in http://www.hep.wisc.edu/~prepost/407/beta/beta.pdf on page 10, it says I could just plot sqrt(N/B^3).
I tried that too but my linear graph looks really messed up. I'm suspecting since my values of B are really small, it blows the numbers up to a really huge extent. But it should still work shouldn't it?
Is there something I'm overlooking?

Thanks a bunch

edit: Also I read from here:

which mentions that "The greatly intensified background in the 22Na spectrum is attributable to the 511 keV annihilation radiation."

Does this mean that the energy spectrum kind of shifts towards the 511 keV side, due to another "mini-peak" in energy?

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If column G is the velocity in m/s, you have velocities that exceed the speed of light - I would expect that you need relativistic formulas there. That will also lead to problems with the approximation you use for F(Z,p).

K is basically inverse momentum, it will have a large numerical value (in SI units) due to the small electron momentum in the denominator. So what - you can express it in units of c/eV if you prefer smaller numbers.