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By — McGraw-Hill Professional
Updated on Apr 25, 2014

#### Problem 1

Suppose that the half-life of a certain radioactive substance is 100 days. You measure the radiation intensity and find it to be x 0 units. What will the intensity x 365 be after 365 days?

#### Solution 1

To determine this, use the equation presented earlier:

x 365 = 0.5 n x 0

where n is the number of half-lives elapsed. In this case, n = 365/100 = 3.65. Therefore:

x 365 = 0.5 3.65 x 0

To determine the value of 0.5 365 , use a calculator with an x y function. This yields the following result to three significant digits:

x 365 = 0.0797 x 0

#### Problem  2

What is the decay constant of the substance described in Problem 18-5?

#### Solution 2

Use the preceding formula for decay constant λ in terms of half-life t 1/2 . In this case, t 1/2 = 100 days. This must be converted to seconds to get the proper result for the decay constant. There are 24 × 60 × 60 = 8.64 × 10 4 s in one day. Thus t 1/2 = 8.64 × 10 6 s, and

λ = 0.69315/(8.64 × 10 6 )

= 8.02 × 10 −8 s −1

#### Problem 3

What is the mean life of the substance described in Problem 18-5? Express the answer in seconds and in days.

#### Solution 3

The mean life τ is the reciprocal of the decay constant. To obtain τ in seconds, divide the numbers in the preceding equation with the numerator and denominator interchanged:

τ= (8.64 × 10 6 )/0.69315

= 1.25 × 10 7

This is expressed in seconds. To express it in days, divide by 8.64 × 10 4 . This gives an answer of approximately 145 days.

Practice problems of these concepts can be found at: Forms of Radiation Practice Test

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