One kilogram of dry air at STP conditions is exposed to 1.00 R of X-rays. One roentgen is defined by Equation 32.1 in Section 32.1. An equivalent definition can be based on the fact that an exposure of one roentgen deposits 8.30 x 10-3 J of energy per kilogram of dry air. Using the two definitions and assuming that all ions produced are singly charged, determine the average energy (in eV) needed to produce one ion in air.
To determine the average energy needed to produce one ion in air, we can use the given information and the definitions provided.
First, let's calculate the amount of energy deposited per kilogram of dry air using the second definition:
Energy deposited per kilogram of dry air = 8.30 x 10^-3 J
Next, we'll find the number of ions produced per kilogram of dry air using the first definition:
Number of ions produced per kilogram of dry air = Exposure in R / Roentgen factor
Since we are given the exposure in R as 1.00 R, we need to find the roentgen factor from Equation 32.1 in Section 32.1.
Since the question doesn't provide Equation 32.1, I'm unable to provide an exact value for the roentgen factor. Please refer to your study material or textbook to find Equation 32.1 and use it to calculate the roentgen factor.
Once you have the roentgen factor, divide the exposure in R by the roentgen factor to obtain the number of ions produced per kilogram of dry air.
Finally, to find the average energy needed to produce one ion in air, divide the energy deposited per kilogram of dry air by the number of ions produced per kilogram of dry air.
Average energy needed to produce one ion in air = Energy deposited per kilogram of dry air / Number of ions produced per kilogram of dry air
Perform the calculations using the provided equations and values to determine the average energy needed to produce one ion in air in eV.