X-raying Echinacea seeds

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What is a typical radiation dose experienced by an Echinacea seed when we x-ray Echinacea fruits to assess seed set?

We usually put the seeds on the bottom tray and the setting 10 s @ 18 kV. According to the documentation on dosage for our x-ray machine 18 kV outputs 292.6 R/h when the dosimeter probe is 57.2 cm away (that's the shelf with 1:1 magnification). The dose unit quote here R is Roetngen.

A little arithmetic can tell us total Roentgens for a ten second exposure:

\( 10 s \frac{1 h}{60 min} \frac{1 min}{60 s} 292.6 \frac{R}{h} \)

In R code, that's

10 * 1/60 * 1/60 * 292.6
## [1] 0.8128

0.8128 R (Roentgen)

We may put the seeds on a higher shelf for more magnification, maybe 1:1.5 or the 1:2. We can enter dosages from each shelf from the documenation on exposure levels by shelf to estimate how much higher the dose is.

lvl <- c(1, 1.5, 2, 3, 4, 5)
RPM <- c(7.815, 20.55, 42.55, 115.45, 232, 397)
data.frame(shelf = lvl, dose = RPM)
##   shelf    dose
## 1   1.0   7.815
## 2   1.5  20.550
## 3   2.0  42.550
## 4   3.0 115.450
## 5   4.0 232.000
## 6   5.0 397.000

The dose on the 2x magnification shelf is RPM[3]/RPM[1] = 5.4447 times greater than the dose on the 1:1 shelf. Doubling the magnification generally should increase the dose by a factor of 5.4. Let's check: the dose on the 4x shelf is RPM[5]/RPM[3] = 5.4524 times greater than the dose on the 2x shelf. Also, the dose on the 3x shelf is RPM[4]/RPM[2] = 5.618 times greater than the dose on the 1.5x shelf. Close.

The expected dose at the stadard settings is 0.82 R on the bottom shelf and 0.8128 * 5.5 = 4.4704, or about 4.5 R on the 2x shelf.

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