EBK COLLEGE PHYSICS
EBK COLLEGE PHYSICS
10th Edition
ISBN: 8220100853050
Author: Vuille
Publisher: CENGAGE L
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Chapter 29, Problem 19P

(a)

To determine

The half-life in seconds.

(a)

Expert Solution
Check Mark

Answer to Problem 19P

The half-life is 6.95×105s .

Explanation of Solution

Given info: Half-life of I131 is 8.04 days.

1day=(24)(3600s)

The half life is,

t1/2=(8.04days)(24)(3600s)1day=6.95×105s

Conclusion:

The half-life is 6.95×105s .

(b)

To determine

The decay constant.

(b)

Expert Solution
Check Mark

Answer to Problem 19P

The decay constant is 9.97×107s1 .

Explanation of Solution

Given info: Half-life of I131 is 6.95×105s .

Formula to calculate the decay constant is,

λ=ln2t1/2

Substitute 6.95×105s for t1/2 in the above equation to get λ .

λ=ln26.95×105s=9.97×107s1

Conclusion:

The decay constant is 9.97×107s1 .

(c)

To determine

The activity in SI unit.

(c)

Expert Solution
Check Mark

Answer to Problem 19P

The activity in SI unit is 1.9×104Bq .

Explanation of Solution

Given info: Activity of I131 is 0.500μCi .

1Ci=3.7×1010Bq

The activity in SI unit is,

R=(0.500×106Ci)(3.7×1010Bq1Ci)=1.9×104Bq

Conclusion:

The activity in SI unit is 1.9×104Bq .

(d)

To determine

The number of I131 .

(d)

Expert Solution
Check Mark

Answer to Problem 19P

The number of I131 is 1.9×1010 .

Explanation of Solution

Given info: Activity of I131 is 0.500μCi .

Formula to calculate the number of I131 is,

N=Rλ

Substitute 0.500μCi for R and 9.97×107s1 for λ in the above equation to get R.

N=0.500μCi9.97×107s1=(0.500×106Ci)(3.7×1010Bq1Ci)9.97×107s1=1.9×1010

Conclusion:

The number of I131 is 1.9×1010 .

(e)

To determine

The number of half-lives completed and activity.

(e)

Expert Solution
Check Mark

Answer to Problem 19P

The number of half-lives completed is 5.

The activity is 0.200mCi .

Explanation of Solution

Section 1:

To determine: The number of half-lives completed.

Answer: The number of half-lives completed is 5.

Explanation:

Given info: Activity ( R0 ) of I131 at a given time is 6.40mCi . Time elapsed is 40.2 days. Half-life of I131 is 8.04 days.

Formula to calculate the number of half-lives is,

n=tt1/2

Substitute 40.2 days for t and 8.04 days for t1/2 in the above equation to get n.

n=40.2days8.04days=5

The number of half-lives completed is 5.

Section 2:

To determine: The activity.

Answer: The activity is 0.200mCi .

Explanation:

Given info: Activity ( R0 ) of I131 at a given time is 6.40mCi . Time elapsed is 40.2 days. Half-life of I131 is 8.04 days.

Formula to calculate the activity is,

R=R02n

Substitute 6.40mCi for R0 and 5 for n in the above equation to get R.

R=6.40mCi25=0.200mCi

The activity is 0.200mCi .

Conclusion:

The number of half-lives completed is 5.

The activity is 0.200mCi

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