11.7. Radiation Protection 663
the square of the distance from the point source, that is
φ∝1
r^2, (11.7.1)
whereris the distance of the measurement point from thepoint source^3.
A point that is worth mentioning here is that for inverse square law to be valid
the radiation should not suffer from significant scattering and absorption in the
medium. In other words this law holds for all types of radiation only in vacuum.
This does not mean that the law is not valid in laboratory environment where the
medium is generally air, since the photons traveling in air suffer very little scattering
and absorption. Therefore x-rays andγ-rays traveling in air do follow inverse square
law to a very good approximation. On the other hand the massive particles, such as
electrons andα-particles, the law does not hold at all. These particles quickly loose
their energy in the medium and removed from the beam after traveling very short
distances. For example, the range of even highly energeticα-particles in air is only
a few centimeters.
Now assume that we have radiation in an environment that does not significantly
absorb or scatter radiation. The question is how we can minimize the dose received
by a person working in that environment. Of course this can be done by maximizing
the distance of the person from the source. Since dose is directly related to the
radiation flux therefore we can also write the inverse square law for dose as
D∝
1
r^2. (11.7.2)
Certainly we can write a similar expression for the exposure as well, that is
X∝
1
r^2. (11.7.3)
Note that this principle of maximizing the distance also holds for radiation that
do not follow inverse square law. However the safe distance in this case is much
smaller than photon beams.
Example:
A person is expected to receive an exposure of 500mRif he stays at a distance
of 12cmfrom the source for 8 hours. What would be the total exposure if
he is asked to stay at a distance of 1.2mfrom the source for the same 8 hours?Solution:
According to equation 11.7.3 the ratio of exposure at two positions is given
by
X 1
X 2=
r 22
r 12.
(^3) As a reminder to the reader, a point source is the one whose dimensions are much smaller than the
distance from the measurement point.