Tuesday Feb. 8, 2011
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The first homework assignment was returned today together with a set of solutions.

A new homework assignment was handed out in class.  This 2 problem set is due next Tuesday, Feb. 15.  To earn full credit on this assignment you will need to destroy your notes from last Thursday's class.  A copy of the Thu., Feb. 3 online lecture notes was handed out to act as replacement notes.

The next several figures show measurements of fair weather conductivity, electric field, and current density made during a field experiment in 1978 in Wyoming.  Simultaneous measurements were made with a variety of different instruments from different research groups.  Instruments were carried up to about 30 km altitude by balloon and measurements were made on the ascent and often during the descent.  Here's a link to the full article (pdf file).



There was generally good agreement among the various measurements of conductivity except for the relaxation time method.  Note the formula used to determine conducitivty (sigma is used in the paper, we have been using lambda in class) is essentially the same as we derived in class last Thursday.

Measurements of electric field (top two plots) and current density (air earth current).  Note that Jz is fairly constant with increasing altitude.

The orange shaded curves are the measurements of Jz, the yellow curve is the product of electric field and conductivity (due to positive charge carriers).  You would expect the measured Jz (which includes both positive and negative charge carriers) to to be roughly twice the positive conductivity times electric field.  The apparent explanation for this descrepancy is shown below (though this seems like too simple a mistake for the researchers to have made):

One of the Jz sensors consisted of two conducting hemispheres insulated from each other.  Charge is induced on the two hemispheres by the ambient electric field.  The figure above shows that the sensor is only capturing half of the charge carries in the atmosphere and therefore only measuring half of the current density, Jz.  There might also be some uncertainty about the effective crossectional area of the current sensor.


Some additional measurements from "the yellow book."  The bottom graph appears to be a reanalysis of the Wyoming data.  The plotted points are conducitivity (positive and negative polarity) times measured electric field.  The plotted values cluster around a value of about 2.5 pA/m2 (note how uniform Jz is with altitude).  The measured value was about twice this, about 5.1 pA/m2.

Now the main part of today's class, the creation of small ions.  Small ions are what gives the atmosphere it's conductivity.  First something must ionize air molecules



Then water vapor molecules cluster around the ions to create "small ions."



Because the positively charged clusters are a little bigger they have slightly lower electrical mobility.
The next figure summarizes the processes that ionize air.

Radioactive materials in the ground emit alpha and beta particles, and gamma rays.  Alpha particles (helium nucleus: two protons and two neutrons) are a strong source of ionization but only in the first few cm above the ground.  Beta particles (electrons) ionize air in a layer a few meters thick.  The effects of gamma radiation extend of 100s of meters.  Cosmic rays are the dominant source of ionization over the ocean and above 1 km over land.

The table below gives an idea of how far these different types of radiation can travel above the ground and also typical ionization rates (from Chapter 11 in "The Earth's Electrical Environment," National Academy of Sciences, 1986 (available online at www.nap.edu/books/0309036801/html/) )

emission type
 range of travel
 ionization rate [ ip/(cm3 sec) ]
alpha particles
 only a few cm above the ground
 not well known
beta particles
 a few meters above the ground
 0.1 to 10
gamma rays
 100s of meters above the ground
1 to 6
radon
 depends on atmospheric conditions
 1 to 20 at 1-2 m above ground
cosmic rays
 1 to 2 ip/(cm3 sec) near the ground


In addition to being a source of atmospheric ionization, radon is a signficant health hazard and is the 2nd leading cause of lung cancer after cigarettes.  There are a couple of articles concerning radon in the articles directory.

The following figure (one side of a class handout) shows a portion of the decay series that ultimately yield isotopes of radon.

Because of its relatively short half like, all the Neptunium in the ground has decayed.  Two isotopes of radon have half lives long enough to be able to diffuse out of the soil and into the air.  Just to add some confusion, the three isotopes of radon are sometimes referred to al radon, actinon, and thoron.  All three isotopes are also known as emanatium.

The article from the World Health Organization gives a typical outdoor radon concentration of 5 to 15 Becquerels/m3 (Bq/m3 ; 1 Becquerel is one disintegration per second ).  We will see what this implies in terms of radon concentration and ion pair production rate.

Since we know the half life we can determine the decay constant for 222Rn.  Then substitute back into the decay rate equation to determine the concentration needed to produce an average outdoors concentration of 10 Bq/m3.




Radon gas decays into solid particles of polonium and lead.  These can attach to dust particles which are then inhaled and trapped in the lungs.  Since the decay products are themselves radioactive long term exposure can ultimately lead to lung cancer.  Radon is apparently the 2nd leading cause of lung cancer in the US after cigarette smoking.

Radon concentration indoors can build to levels that are much higher than normally found outdoors.  An extreme case is mentioned below.