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Initially 100 milligrams of a radioactive substance was present. After 8 hours the mass had decreased by 2%. If the rate of decay is proportional to the amount of the substance present at time t, determine the half-life of the radioactive substance. (Round your answer to one decimal place.)

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Numenius

Answer:

The half life of the radioactive substance is 277 hours.

Step-by-step explanation:

initial mass, No = 100 mg

mass decayed = 2% = 2 mg

Mass remained , N = 98 mg

time, t = 8 hours

Let the half life is T.

Use the equation of radioactivity

[tex]N = No\times e^{\frac{-0.693 t}{T}}\\\\98 = 100 \times e^{\frac{-0.693\times 8}{T}}\\\\0.98 = e^{\frac{-5.54}{T}}\\\\ln 0.98 = -\frac{5.54}{T}\\\\-0.02= -\frac{5.54}{T}\\\\T = 277 hours[/tex]  

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