Answer to Question #2419 Submitted to "Ask the Experts"

Q

I know that 1 kGy = 1 kJ/kg = 1 kW x s/kg, so that kGy x kg = 1 kW x s, or 1 kW of x-ray power = (kGy x kg)/s. Now, assuming a point source of x rays, the x-ray power is distributed uniformly over the surface area of 4 x pi x r², and we can write that as:

1 kW/(4 x pi x r²) = (1/4pi)(kGy x kg)/r².

Finally, my question is, how do I interpret the units on the right-hand side, i.e., (kGy kg)/m², assuming the distance r is in meters?

A

With the manipulation of units that you carried out, one must be careful to keep in mind the specific physical quantities to which they apply. (I think your last equation is missing reciprocal seconds on the right, but that is not an issue here.)

For a point source, generating 1 kW of x rays uniformly in all directions, the intensity I of the radiation at a distance r meters is given by

I = 1/(4 pi r²) kW/m²,

as expressed by the left-hand side of your last equation. Intensity expresses the rate of radiation energy flow per unit area. Since 1 kW = 1 kJ/s, you can also write for the intensity from the 1-kW source

I = 1/(4 pi r²) kJ/(m2 s).

The trouble with interpreting units in your last equation comes when one introduces 1 kGy = 1 kJ/kg and applies it to the radiation field. While dimensionally correct, the energy kJ used in the definition of the Gy refers by definition to an energy that is absorbed in some dose specification. It is not the energy that determines the intensity of the radiation field. So I think you should not write what you did in your opening statement, namely, 1 kW of x-ray power = (kGy x kg)/s. It is inappropriate to use Gy as a unit for anything other than absorbed dose.

Perhaps a similarity can be found in the use of the unit of reciprocal time, s^-1. It applies to the activity of a radioactive source (Bq) as well as to the frequency of an electromagnetic wave (Hz). However, 1 Bq is not interchangable with 1 Hz in describing things. Neither is 1 kGy kg the "same" as 1 kJ.

James E. Turner, CHP, PhD