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Chapter 24: 24.112 CP (page 1106)

In the 1950s, radioactive material was spread over the land from aboveground nuclear tests. A woman drinks some contaminated milk and ingests 0.500 g of 90Sr, which is taken up by bones and teeth and not eliminated.

(a) How muchS90r(t1/2=29yr)is present in her body after 10yr ?

(b) How long will it take for 99.9% of the90Sr to decay?

Short Answer

Expert verified

(a) The amount 90Sr of that is present in her body after ten years isNt=0.0394g90Sr.

(b) The time required for 99.9% of the 90Sr to decay is t=125.52 yr.

Step by step solution

01

Half-life

The half-life of a radioactive substance is defined as the amount of time required for the decay of half the initial amount of a substance. Half-life is denoted by t12 .

Radioactive decay is a first-order reaction. The expression for half-life is given below.

t1/2=0.693k

Where, k is the decay constant.

02

Find the decay constant from the half-life

Identify the constant (k) using the formula for half-life.

t1/2=ln2k鈫�k=ln2t1/2k=ln2t1/2=ln229yr=鈥�0.023902yr-

03

Amount of 90Sr present after 10 years

Radioactive decay us a first order reaction. Therefore, we will use the following equation to estimate the amountof 90Sr present in the woman鈥檚 body after 10 years.

Nt=N0e-ktNt=0.0500脳e-0.023902鈥�yr-脳10yr鈥�gNt=0.0394g

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