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 1 mol of gas, if a Geiger counter is filled with 9846 Pa of argon gas at room temperature ( T = 21.1 °C ) , what is the density, rho , of the gas in this Geiger tube?

Answer 1

Answer:

$0.16098\times 10^{-3}\ g/cm^3$

Explanation:

P =Pressure = 9846 Pa

V = Volume

n = Amount of substance = 1

T = Temperature = 21.1°C

$\rho$ = Density

R = Gas constant = 8.314 J/mol K

M = Molar mass of argon = 40 g/mol

From ideal gas law we have the relation

$PV=nRT$

Multiply density on both sides

$PV\rho=nR\rho T\\\Rightarrow PM=nR\rho T\\\Rightarrow \rho=\dfrac{PM}{nRT}\\\Rightarrow \rho=\dfrac{9846\times 40\times 10^{-3}}{8.314\times (21.1+273.15)}\\\Rightarrow \rho=0.16098\ kg/m^3\\\Rightarrow \rho=0.16098\times 10^{-3}\ g/cm^3$

The density of argon gas is $0.16098\times 10^{-3}\ g/cm^3$