Suppose the amount of a certain radioactive substance in a sample decays from to over a period of days. Calculate the half life of the substance. Round your answer to significant digit.

The given question is incomplete, the complete question is:

Suppose the amount of a certain radioactive substance in a sample decays from 1.30 mg to 100. ug over a period of 29.5 days. Calculate the half life of the substance Round your answer to 2 significant digits.

The correct answer is 7.974 days.

Explanation:

Based on the given question, the concentration of a radioactive substance present in a sample get decays to 100 micro grams from 1.30 milligrams in 29.5 days. There is a need to find the half-life of the substance.  

Radioactive decay is an illustration of first order reaction.  

K = (2.303 / t) log [a/(a-x)]

Here a is 1.30 mg and (a-x) is 100 micrograms = 100 * 10^-3 mg or 0.1 mg, and t is 29.5 days. Now putting the values we get,  

K = (2.303 /29.5)log (1.30/0.1)

= 2.303/29.5 log13

= 2.303/29.5 * 1.1139

K = 0.0869

The half-life or t1/2 is calculated by using the formula, 0.693 / K

= 0.693 / 0.0869

= 7.974 days.  

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