As part of the software display on the Model 1950 Alpha Particle Counter, the LLD is an automatic
function of the data compute button. Two major factors effect the LLD: time and background of the
tool. The longer the count, and the lower the background, the better the LLD.

The Lower Limit of Detection (LLD) is essentially a reference to both how low a sample can be counted
over background, and at what level of confidence that reading is given. If the sample counts well above
the background level of the tool, there really is no need to refer to the LLD. However, if the sample is
counting at or near the background level of the tool, then the LLD formula becomes very important.

On the pages LLD, The Formula and LLD, The Equation, we see how we derive our variables for
determining the Lower Limit of Detection. Here, let's apply the LLD to a typical sample count from
our Model 1950 to see how it works:

Assume that the counting time for measuring the background of the counter and the counting time for
measuring the sample are equal. Also assume that the background is 3 alphas per hour for the total
1000 cm² area (0.003 a/cm²/hr). The background and sample were each counted for 4 days, which
comes out to 96 hours each (24 hours x 4 days = 96 hours). At 3 alphas per hour background over
96 hours, we can say 96 hours x 3 = 288 alpha counts attributable to the background of the tool.

Using the LLD Equation we can state the following:

LLD = 4.66 x square root of 288, = 4.66 x 17 = 79 counts above background, over 96 hrs, 1000 cm²

79 divided by 96 hours = 0.82 alpha counts above background, over 1000 square centimeters.

0.82 divided by 1000 sq. centimeters = 0.0008 alpha counts above background, per hr, per cm².

Therefore, the Lower Limit of Detection is defined as 0.0008 a/cm²/hr.
 

Now, let's assume the same conditions above, only we count for one day (24 hours).

24 hours x 3 alphas per hour = 72 alpha counts attributable to the background of the tool.

LLD = 4.66 x square root of 72 = 4.66 x 8.5 = 40 counts above background, over 24 hrs, 1000 cm²

40 divided by 24 hours = 1.7 alpha counts above background, over 1000 square centimeters.

1.7 divided by 1000 sq. centimeters = 0.002 alpha counts above background, per hr, per cm².

Therefore, the Lower Limit of Detection is defined as 0.002 a/cm²/hr.

For comparison:
Count Interval             LLD
96 hours                       0.0008 a/cm²/hr
24 hours                       0.002 a/cm²/hr.

Conclusion: The longer the counting time, the more accurate your data (more sensitive) will be to determine
the activity of your sample, most notably when the sample counts and background counts are nearly the same.

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copyright Alpha Sciences Inc. 2001