Final answer:
To calculate the Townsend first ionization coefficient α and the minimum 'pd' value, formulas involving the given exponential constants and the secondary ionization coefficient γ are used, followed by finding the breakdown voltage by multiplying 'pd' by the pressure.
Step-by-step explanation:
The question is about the determination of the Townsend first ionization coefficient α for an exponential function given constants A = 15 and B = 360 with an electric field to pressure ratio (E/p) of 150 V/cm-torr. The question further asks to calculate the minimum product of gas pressure (p) and electrode distance (d), denoted as 'pd', and the corresponding minimum breakdown voltage, considering the secondary ionization coefficient (γ) to be 10⁻⁴.
To find α, we use the formula α = A × exp(-B / (E/p)), where A and B are constants, and E/p is the electric field to pressure ratio. Substituting the given values, α = 15 × exp(-360 / 150), we can calculate α. Next, to find the minimum value of 'pd', we use the relationship αd = ln(1 + 1/γ). With γ = 10⁻⁴, we solve for 'pd'. Finally, the minimum breakdown voltage V is found by multiplying the minimum 'pd' value by the pressure p.
Furthermore, using the context provided on photoelectrons, when a given radiation deposits energy in material, ion pairs are formed if the radiation is ionizing, like in a Geiger tube, and the energy required for each ion pair creation can be used to determine the number of ion pairs formed from the total deposited energy.