Question

A Geiger–Muller tube is a type of gas‑filled radiation detector. It can detect particles like X‑rays, alpha particles, and beta rays (electrons). This is useful in quantizing the activity of a radioactive source or determining if an area containing radioactive material is safe to enter. Assuming that you have 1mol of gas, if a Geiger counter is filled with 9674 Pa of argon gas at room temperature (T=23.3 °C), what is the density,

ρ, of the gas in this Geiger tube?

Answer 1

To find the density, , we need to find the volume of the 1 mol of the gas at the given pressure and temperature. Since the pressure is about 1/10 of atmospheric pressure while the temperature is room temperature, we can expect that the ideal gas law is a good approximation of the equation of state i.e. the relation between pressure, volume and temperature is given by

where p is pressure, V is volume, n is the number of moles of the gas, R is gas constant whose value is 8.314 J/(K.mol) and T is absolute temperature. So, in the situation given in the question we have

  

This gives cubic-meter. This volume contains 1 mol of the gas. So, the density is

where M is mass of one mol of argon gas. To find M we use the fact that Argon is mono-atomic, the mass of 1 atom of argon is    Kg and 1 mol has approximately particles, which in our case are atoms. So, M is approximately 0.04 Kg .

We find  

in units of Kg/(cubic-meter) .