General, Organic, and Biological Chemistry
General, Organic, and Biological Chemistry
7th Edition
ISBN: 9781285853918
Author: H. Stephen Stoker
Publisher: Cengage Learning
Question
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Chapter 11, Problem 11.27EP

(a)

Interpretation Introduction

Interpretation:

Half-life of the radionuclide has to be determined if after 5.4 days, 1/16 fraction of undecayed nuclide is present.

Concept Introduction:

Radioactive nuclides undergo disintegration by emission of radiation.  All the radioactive nuclide do not undergo the decay at a same rate.  Some decay rapidly and others decay very slowly.  The nuclear stability can be quantitatively expressed by using the half-life.

The time required for half quantity of the radioactive substance to undergo decay is known as half-life.  It is represented as t1/2.

The equation that relates amount of decayed radioactive material, amount of undecayed radioactive material and the time elapsed can be given as,

(Amountofradionuclideundecayedafternhalflives) =  (Originalamountofradionuclide)  x  (12n)

(a)

Expert Solution
Check Mark

Answer to Problem 11.27EP

Half-life of the radionuclide is 1.4 days.

Explanation of Solution

Number of half-lives can be determined as shown below,

(12n) = 116(12n) = 1242n = 24

As the bases are equal, the power can be equated.  This gives the number of half-lives that have elapsed as 4 half-lives.

In the problem statement it is given that the time is 5.4 days.  From the number of half-lives elapsed and the total time given, the length of one half-life can be calculated as shown below,

5.4 days   x  (1 half-lifet1/2) = 4 half-lives t1/2 = 5.4 days4 = 1.4days

Therefore, the half-life of the given sample is determined as 1.4 days.

Conclusion

Half-life of the given sample is determined.

(b)

Interpretation Introduction

Interpretation:

Half-life of the radionuclide has to be determined if after 5.4 days, 1/64 fraction of undecayed nuclide is present.

Concept Introduction:

Radioactive nuclides undergo disintegration by emission of radiation.  All the radioactive nuclide do not undergo the decay at a same rate.  Some decay rapidly and others decay very slowly.  The nuclear stability can be quantitatively expressed by using the half-life.

The time required for half quantity of the radioactive substance to undergo decay is known as half-life.  It is represented as t1/2.

The equation that relates amount of decayed radioactive material, amount of undecayed radioactive material and the time elapsed can be given as,

(Amountofradionuclideundecayedafternhalflives) =  (Originalamountofradionuclide)  x  (12n)

(b)

Expert Solution
Check Mark

Answer to Problem 11.27EP

Half-life of the radionuclide is 0.90 day.

Explanation of Solution

Number of half-lives can be determined as shown below,

(12n) = 164(12n) = 1262n = 26

As the bases are equal, the power can be equated.  This gives the number of half-lives that have elapsed as 6 half-lives.

In the problem statement it is given that the time is 5.4 days.  From the number of half-lives elapsed and the total time given, the length of one half-life can be calculated as shown below,

5.4 days   x  (1 half-lifet1/2) = 6 half-lives t1/2 = 5.4 days6 = 0.90day

Therefore, the half-life of the given sample is determined as 0.90 day.

Conclusion

Half-life of the given sample is determined.

(c)

Interpretation Introduction

Interpretation:

Half-life of the radionuclide has to be determined if after 5.4 days, 1/256 fraction of undecayed nuclide is present.

Concept Introduction:

Radioactive nuclides undergo disintegration by emission of radiation.  All the radioactive nuclide do not undergo the decay at a same rate.  Some decay rapidly and others decay very slowly.  The nuclear stability can be quantitatively expressed by using the half-life.

The time required for half quantity of the radioactive substance to undergo decay is known as half-life.  It is represented as t1/2.

The equation that relates amount of decayed radioactive material, amount of undecayed radioactive material and the time elapsed can be given as,

(Amountofradionuclideundecayedafternhalflives) =  (Originalamountofradionuclide)  x  (12n)

(c)

Expert Solution
Check Mark

Answer to Problem 11.27EP

Half-life of the radionuclide is 0.68 day.

Explanation of Solution

Number of half-lives can be determined as shown below,

(12n) = 1256(12n) = 1282n = 28

As the bases are equal, the power can be equated.  This gives the number of half-lives that have elapsed as 8 half-lives.

In the problem statement it is given that the time is 5.4 days.  From the number of half-lives elapsed and the total time given, the length of one half-life can be calculated as shown below,

5.4 days   x  (1 half-lifet1/2) = 8 half-lives t1/2 = 5.4 days8 = 0.68day

Therefore, the half-life of the given sample is determined as 0.68 day.

Conclusion

Half-life of the given sample is determined.

(d)

Interpretation Introduction

Interpretation:

Half-life of the radionuclide has to be determined if after 5.4 days, 1/1024 fraction of undecayed nuclide is present.

Concept Introduction:

Radioactive nuclides undergo disintegration by emission of radiation.  All the radioactive nuclide do not undergo the decay at a same rate.  Some decay rapidly and others decay very slowly.  The nuclear stability can be quantitatively expressed by using the half-life.

The time required for half quantity of the radioactive substance to undergo decay is known as half-life.  It is represented as t1/2.

The equation that relates amount of decayed radioactive material, amount of undecayed radioactive material and the time elapsed can be given as,

(Amountofradionuclideundecayedafternhalflives) =  (Originalamountofradionuclide)  x  (12n)

(d)

Expert Solution
Check Mark

Answer to Problem 11.27EP

Half-life of the radionuclide is 0.54 day.

Explanation of Solution

Number of half-lives can be determined as shown below,

(12n) = 11024(12n) = 12102n = 210

As the bases are equal, the power can be equated.  This gives the number of half-lives that have elapsed as 10 half-lives.

In the problem statement it is given that the time is 5.4 days.  From the number of half-lives elapsed and the total time given, the length of one half-life can be calculated as shown below,

5.4 days   x  (1 half-lifet1/2) = 10 half-lives t1/2 = 5.4 days10 = 0.54day

Therefore, the half-life of the given sample is determined as 0.54 day.

Conclusion

Half-life of the given sample is determined.

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Chapter 11 Solutions

General, Organic, and Biological Chemistry

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