A container filled with air at room temperature and pressure is exposed to a beam of X-rays which ionizes a small fraction of the molecules inside. The negative ions are actually 0, molecules with an extra electron. For the purposes of this problem, however, you may treat all the molecules as having the same molecular weight, somewhere between that of O2 and N2. Let the box be 10 cm x 10 cm x 2 cm. The two 10 cm x 10 cm faces are metal, whereas the rest of the box is made of insulating material. A potential of 1 kV is applied across the conducting ends causing a current of 1.5 µA to flow. (a) What is the conductivity of this weakly ionized gas? (b) If the mean collision time z is 2 x 10-10 s, what fraction of the molecules in the gas are ionized? (Assume equal numbers of positive and negative singly charged ions.)

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3 Ionic Conductivity
A container filled with air at room temperature and pressure is exposed to a beam of X-rays which ionizes a small fraction
of the molecules inside. The negative ions are actually 0, molecules with an extra electron. For the purposes of this
problem, however, you may treat all the molecules as having the same molecular weight, somewhere between that of O,
and N2.
Let the box be 10 cm x 10 cm x 2 cm. The two 10 cm x 10 cm faces are metal, whereas the rest of the box is made of
insulating material. A potential of 1 kV is applied across the conducting ends causing a current of 1.5 µA to flow.
(a) What is the conductivity of this weakly ionized gas?
(b) If the mean collision time r is 2 x 10-10 s, what fraction of the molecules in the gas are ionized?
(Assume equal numbers of positive and negative singly charged ions.)
Transcribed Image Text:3 Ionic Conductivity A container filled with air at room temperature and pressure is exposed to a beam of X-rays which ionizes a small fraction of the molecules inside. The negative ions are actually 0, molecules with an extra electron. For the purposes of this problem, however, you may treat all the molecules as having the same molecular weight, somewhere between that of O, and N2. Let the box be 10 cm x 10 cm x 2 cm. The two 10 cm x 10 cm faces are metal, whereas the rest of the box is made of insulating material. A potential of 1 kV is applied across the conducting ends causing a current of 1.5 µA to flow. (a) What is the conductivity of this weakly ionized gas? (b) If the mean collision time r is 2 x 10-10 s, what fraction of the molecules in the gas are ionized? (Assume equal numbers of positive and negative singly charged ions.)
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