What is the purpose of counting the background radioactive decays and subtractin

Question

What is the purpose of counting the background radioactive decays and subtracting the background counts-per-minute from our measured counts-per-minute? Was your graph of 40^K disintegrations per minute vs. mass linear? Should it have been linear? If it was not linear, explain why you think it wasn't. Using the formulas on page 1, calculate the predicted number of 40^K disintegrations per minute for a 1.00 g sample of natural KCI (s). The data you'll need for this are: The half-life of 40^K is 1.248 times 10^9 years The natural abundance of 40^K is 0.0117% The atomic masses of K and Cl Avogadro's number - 6 022 times 10^23 The two formulas on page 1 The number of minutes in 1 year

Explanation / Answer

1. The background is measured for the sample is performed to subtract the natural radioactivity (which is around us - particulary gamma radiation) hitting the detector . There are cosmic radiations and other natural radioactivity which is always present and this activity has to be calculated and subtracted from the actual sample, otherwise it will give a positive error.

2. The graph of dpm vs the mass is linear becuse radioactive decay is a first order and the radioactivity depends on the mass of the mass. Higher the mass of the radioactive material, more is the activity (beacuse of the presence of more atoms. The graph may not be linear (if the case is so) because the measurement of change in mass has the to be detected by the sensitive measurement devise.

4. A = N

t1/2 = 1.248x109 years = 1.248x109 x 365.25 x 24 x 60 = 6.56 x 1014 min

= 0.693/t1/2 = 0.693/6.56 x 1014 min = 0.105x 10-14 min-1

N = 0.00117 x (1g/ 74.5 g/mol) x 6.023x1023 molecules/mol = 9.45x1018 molecules of KCl

A = N = 0.105x 10-14 min x 9.45x1018 = 0.99x 104 dpm = 9900 dpm.

So the calculate amount of radioactivity of 1g of KCl is 9900 dpm

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