Problem statement: A thick target of 55Mn is irradiated with deutrons with current $I$ during a time $T$. Most of the reactions result in 56Mn, which then decays with half-life $t_{1/2}$. Calculate the number of active 56Mn nuclei at the end of the irradiation under the assumption that the deutrons have range $R$ and that the mean value of the cross-section over this range is $\sigma$.

Following the question there are some numbers given, and the range $R$ is given in units of mg/cm$^2$.

I cannot find a consistent explanation of what this range is defined as. In my understanding it is the maximum distance a particle can go in a material until it runs out of energy. But the units makes no sense.

I've done a similar calculation where I calculated the reaction rate, and solved the ODE $$ \frac{dN}{dt} = (\text{reaction rate}) - \lambda N, $$ where $N$ is the number of active nuclei.

Some explanation of this range and how to use it in this calculation is appreciated.

  • $\begingroup$ Another useful word is a "stopping power" of matter. $\endgroup$ May 26, 2018 at 14:58
  • $\begingroup$ The stopping power is certainly related to range. But, range just tells you how far into the film the beam/individual ions get. So, with a quick calculation you know how many nuclei might interact with the beam in total. $\endgroup$
    – Jon Custer
    May 26, 2018 at 15:02
  • $\begingroup$ I would appreciate if you could elaborate on how to perform the "quick calculation". And why is range expressed in mass per unit area if it is actually a distance? $\endgroup$ May 26, 2018 at 15:14
  • $\begingroup$ Look at a Wikipedia entry about "stopping power", please. $\endgroup$ May 26, 2018 at 16:40
  • $\begingroup$ I've added the homework-and-exercises tag. In the future, please use this tag on this type of question. $\endgroup$
    – user4552
    May 26, 2018 at 17:11

1 Answer 1


While we usually think of "range" as distance--so dimensions of length and units of meters--that's not totally practical in nuclear physics. When considering the passage of a particle through matter, the areal density of matter per unit distance is important--and that is given by density, $\rho$, (inverse length cubed).

So, if you are given $R$ in mass per unit area (mg/cm^2 is a little unusual):

$$ r = \frac R {\rho} $$

which is:

$$ {\mathrm{meters}} = \frac{\mathrm{kg/m^2}}{ {\mathrm{kg}}/ {\mathrm m^3}} $$.

Since energy loss is a random process, one can't say $R$ is an absolute maximum--but there are many ionizing interactions contributing the energy loss, so it's pretty reliable. Please see this table for your target nuclei:



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.