How Many Ion Pairs Will a Beta Particle Produce Inside a Helium-Filled Geiger Tube?

How can we calculate the number of ion pairs produced by a beta particle passing through a helium-filled Geiger tube? The beta particle is estimated to produce approximately 4689 ion pairs inside the helium-filled Geiger tube. To calculate this, we can use the concept of ionization energy and the energy of the beta particle.

Ionization Energy in Helium Gas

The energy required to produce an ion pair (W) is typically around 33.97 electron volts (eV) in helium gas. This means that for every ion pair produced, 33.97 eV of energy is needed. To convert this value to megaelectron volts (MeV), we divide by 1 million: W = 33.97 eV / 1,000,000 = 0.00003397 MeV.

Calculating Number of Ion Pairs

Given that the kinetic energy of the beta particle is 0.159 MeV, we can calculate the number of ion pairs produced as follows: Number of ion pairs = (Kinetic energy of the beta particle) / (Ionization energy per ion pair). Therefore, Number of ion pairs = 0.159 MeV / 0.00003397 MeV/ion pair ≈ 4689 ion pairs.

Therefore, the beta particle is estimated to produce approximately 4689 ion pairs inside the helium-filled Geiger tube.

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