I have been reading a few papers on radiation therapy and have come to something I do not understand. In some of the papers they express the dose rate in the following units

$$\frac{MeV}{g\space Bq\space s}$$

I know that the dose rate of a point source to some material is given by $$\dot D=\dot {\phi} E \frac{\mu_{e_n}}{\rho}$$ From this relation the units are $$\frac{MeV}{g\space s}\space or \space \frac{Gy}{h}$$ my question is where do the units of inverse becquerels and seconds come from? I have seen online that they are used as units of photon yield, but these sources gave no background as to why the units were being used. A suggestion to a text with a derivation would be very helpful

• On the typesetting of units. First it is typical to set units in an upright font (using \mathrm or \text), and second you should forcibly separate distinct units using either a thing space (\,) or a center dot (cdot) so that their concatanation can't be mistaken for a prefix and a unit. – dmckee --- ex-moderator kitten Aug 30 '19 at 21:13
• Please define your notation such as $\dot{\phi}$ and $\mu_{e_n}$. – user4552 Aug 31 '19 at 14:36

“Bq” are units of activity: decays per second.

“Bq s “ are the units for a total number of decays.

“MeV / g” is the total amount of energy deposited normalized by the mass of some target object. We tend to think of this as “dose”.

“MeV / (g Bg s)” is then the energy in that volume deposited per decay.

It’s not really an exposure dose as we normally think of those. Rather, it’s a constant you’d use to convert a particular exposure (in Bq s) to dose.

This isn’t a rate, and you shouldn’t be misled by the /s to think it is.

• okay so its the dose per decay. I am assuming that experimentally you can determine the total number of decays. Another question is how does one theoretically calculate it? – Stripers247 Aug 31 '19 at 15:50