a Geiger ionization chamber contains 60 cubic cm of air and records 500 mR/min. calculate (a). the current produce by the chamber (b). the total number of ion pairs produced per hour of exposure.
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V=60 cm³
500 mR/min= 500•10⁻³/60 = 8.33•10⁻³ R/s,
the charge in 1 cm³ is
q= 8.33•10⁻³•3.33•10⁻¹º =2.78•10⁻¹² C
in chamber
Q=2.78•10⁻¹²•60 =1.67•10⁻¹º C
I=Q/t= 1.67•10⁻¹º A
1 R produces 2.08 •10⁹ pairs of ions in 1 cm³
N= 8.33•10⁻³•2.08 •10⁹ = 1.73•10⁷ pairs per second
To calculate the current produced by the Geiger ionization chamber, you need to use the formula:
Current (I) = Radiation dose rate (D) / Charge collected per ion pair (Q)
Given that the chamber records 500 mR/min (milliroentgens per minute), we first need to convert this value to Coulombs (C) per minute.
1 Roentgen (R) = 2.58 x 10^-4 C/kg
1 mR = 10^-3 R
Therefore, 500 mR = 500 x 10^-3 R = 500 x 10^-3 x 2.58 x 10^-4 C/kg = 0.129 C/kg
Now, we need to calculate the charge collected per ion pair (Q) using the known air density (ρ) and ion pair production energy (W).
Air density (ρ) = 1.205 kg/m^3 (at standard conditions)
Volume of the chamber (V) = 60 cm^3 = 60 x 10^-6 m^3
Mass of air in the chamber (m) = ρ x V = 1.205 kg/m^3 x 60 x 10^-6 m^3 = 0.0723 g = 0.0723 x 10^-3 kg
Ion pair production energy (W) for air = 33.97 eV
1 electron charge = 1.6 x 10^-19 C
1 eV = 1.6 x 10^-19 C
Therefore, Charge collected per ion pair (Q) = W / (1 eV) x (1.6 x 10^-19 C) = 33.97 eV / 1 x (1.6 x 10^-19 C) = 2.123 x 10^-18 C
Now, using the above values, we can calculate the current produced by the chamber:
Current (I) = Radiation dose rate (D) / Charge collected per ion pair (Q)
I = 0.129 C/kg / (2.123 x 10^-18 C) ≈ 6.08 x 10^16 A
Therefore, the current produced by the chamber is approximately 6.08 x 10^16 Amperes (A).
To calculate the total number of ion pairs produced per hour of exposure, we need to use the formula:
Number of ion pairs (N) = Current (I) x Charge collected per ion pair (Q) x Time (t)
Given that the exposure time is 1 hour = 60 minutes, we have:
Number of ion pairs (N) = 6.08 x 10^16 A x 2.123 x 10^-18 C x 60 minutes ≈ 0.783 x 10^16
Therefore, the total number of ion pairs produced per hour of exposure is approximately 0.783 x 10^16 ion pairs.