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My mass spectrometry textbook gives the following example:

Calculating sensitivity Magnetic sector instruments are specified to have a sensitivity of about $4 \times 10^{-7} C \ \mu g^{-1}$ for the molecular ion of methylstearate, $m/z \ 298$, at $R = 1000$ in $70 \ eV$ EI mode. One microgram of methylstearate is equivalent to $3.4 \times 10^{-9} mol$ or $2.0 \times 10^{15}$ molecules. The charge of $4 \times 10^{-7} C$ corresponds to $2.5 \times 10^{12}$ electron charges of $1.6 \times 10^{-19} C$ each. Vice versa, in dividing the number of molecules per microgram by the number of charges at the detector we may conclude that only one out of $800$ molecules is finally detected.

I have three questions:

  1. What is $R = 1000$ supposed to be? The author never mentioned such a quantity at any previous point in the textbook.

  2. How did the author calculate that the charge of $4 \times 10^{-7} C$ corresponds to $2.5 \times 10^{12}$ electron charges of $1.6 \times 10^{-19} C$ each? Or is this just a fact that he has knowledge of?

  3. How did the author calculate the last part:

Vice versa, in dividing the number of molecules per microgram by the number of charges at the detector we may conclude that only one out of $800$ molecules is finally detected.

?

I would greatly appreciate it if people could please take the time to clarify this.

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  • $\begingroup$ @EdV Yes, but I'm referring to the converse of the calculation; that's the point of the author's statement in the second question. We start with the information that the instruments are specified to have a sensitivity of about $4 \times 10^{-7} C \ \mu g^{-1}$. The author then decomposes this into $2.5 \times 10^{12}$ electron charges of $1.6 \times 10^{-19} C$ each. The point of question 2 is, starting with the value of $4 \times 10^{-7} C \ \mu g^{-1}$, how did the author induce that this is $2.5 \times 10^{12}$ electron charges of $1.6 \times 10^{-19} C$ each? ... $\endgroup$
    – The Pointer
    Jun 20, 2019 at 16:54
  • $\begingroup$ ... After all, we could have used any other combination of $x$ and $y$ such that $x + y = 4 \times 10^{-7} C$ - not necessarily $2.5 \times 10^{12}$ and $1.6 \times 10^{-19} C$. So, the question becomes, how did the author get the specific values $2.5 \times 10^{12}$ and $1.6 \times 10^{-19} C$? $\endgroup$
    – The Pointer
    Jun 20, 2019 at 17:01
  • $\begingroup$ @EdV Ok, I understand now. Thank you very much for the clarification. You should have posted it as an answer so that I could accept it, haha. And yes, it seems that the quantity $R$ might remain a mystery. $\endgroup$
    – The Pointer
    Jun 20, 2019 at 17:26

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