A particle of ionizing radiation creates 7500 ion pairs in the gas inside a Geig

Question

A particle of ionizing radiation creates 7500 ion pairs in the gas inside a Geiger tube as it passes through. Randomized Variables N = 7500 ion pairs What is the minimum energy, in joules, that was deposited if 30.0 eV is required to create each ion pair? If all of this energy is converted to thermal energy in the gas, what is its temperature increase in degrees Celsius, assuming it consists of 50.0 cm^3 of monatomic ideal gas at 0.250-atm pressure? You may assume the temperature change is small and the gas is at 20 degree C.

Explanation / Answer

Part (A) :
E =30 eV , 1e =1.6*10^-19 C, N =7500

Etot = 7500*30*1.6*10^-19 = 3.6*10^-14 J

Part (B) :

P = 0.25 atm , 1atm =1.01*10^5 Pa, V = 50 cm^3, T =20 oC = 20+273 = 293 K

From ideal ga equation PV = NkBT

NKB = PV/T

Etot = (3/2) NKB(DT)

3.6*10^-14 =(1.5*0.25*1.01*10^5*50*10^-6/293)(DT)

change in temperature = 5.57*10^-12 oC

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