Q1 PE - College Physics (Urone)

Question

The energy of \(30.0\,{\rm{eV}}\) is required to ionize a molecule of the gas inside a Geiger tube, thereby producing an ion pair. Suppose a particle of ionizing radiation deposits \(0.500\,{\rm{MeV}}\) of energy in this Geiger tube. What maximum number of ion pairs can it create?

Step-by-Step Solution

Answer

Maximum number of ion pairs is obtained as: \(1.667 \times {10^4}\,{\rm{pairs}}\).

Step 1: Define Radioactivity

The spontaneous emission of radiation in the form of particles or high-energy photons as a result of a nuclear process is known as radioactivity.

Step 2: Evaluating the maximum number of ion pairs

The required energy to ionize the molecule is given as:

\({E_{ion}} = 30\,{\rm{eV}}\)

The energy of the radiation in the Geiger tube is given as:

\({E_{rad}} = 0.5\,{\rm{MeV}}\)

The number of ion pairs, is then obtained as:

\(\begin{align}Number{\rm{ }}of{\rm{ }}ion{\rm{ }}pairs{\rm{ }} &= \frac{{The{\rm{ }}energy{\rm{ }}of{\rm{ }}the{\rm{ }}radiation{\rm{ }}in{\rm{ }}the{\rm{ }}Geiger{\rm{ }}tube}}{{The{\rm{ }}energy{\rm{ }}for{\rm{ }}ionize{\rm{ }}molecule}}\\ &= \frac{{0.5 \times {{10}^6}\,eV}}{{30\,eV}}\\ &= 1.667 \times {10^4}\,pairs\end{align}\)

Therefore, the maximum number of ion pairs are: \(1.667 \times {10^4}\,{\rm{pairs}}\).