General, Organic, and Biological Chemistry Seventh Edition
General, Organic, and Biological Chemistry Seventh Edition
7th Edition
ISBN: 9781305767867
Author: H. Stephan Stoker
Publisher: Cengage Learning
Question
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Chapter 11, Problem 11.28EP

(a)

Interpretation Introduction

Interpretation:

Half-life of the radionuclide has to be determined if after 3.2 days, 1/8 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 11.28EP

Half-life of the radionuclide is 1.1 days.

Explanation of Solution

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

(12n) = 18(12n) = 1232n = 23

As the bases are equal, the power can be equated.  This gives the number of half-lives that have elapsed as 3 half-lives.

In the problem statement it is given that the time is 3.2 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,

3.2 days   x  (1 half-lifet1/2) = 3 half-lives t1/2 = 3.2 days3 = 1.1days

Therefore, the half-life of the given sample is determined as 1.1 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 3.2 days, 1/128 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 11.28EP

Half-life of the radionuclide is 0.46 day.

Explanation of Solution

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

(12n) = 1128(12n) = 1272n = 27

As the bases are equal, the power can be equated.  This gives the number of half-lives that have elapsed as 7 half-lives.

In the problem statement it is given that the time is 3.2 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,

3.2 days   x  (1 half-lifet1/2) = 7 half-lives t1/2 = 3.2 days7 = 0.46day

Therefore, the half-life of the given sample is determined as 0.46 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 3.2 days, 1/32 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 11.28EP

Half-life of the radionuclide is 0.64 day.

Explanation of Solution

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

(12n) = 132(12n) = 1252n = 25

As the bases are equal, the power can be equated.  This gives the number of half-lives that have elapsed as 5 half-lives.

In the problem statement it is given that the time is 3.2 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,

3.2 days   x  (1 half-lifet1/2) = 5 half-lives t1/2 = 3.2 days5 = 0.64day

Therefore, the half-life of the given sample is determined as 0.64 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 3.2 days, 1/512 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 11.28EP

Half-life of the radionuclide is 0.36 day.

Explanation of Solution

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

(12n) = 1512(12n) = 1292n = 29

As the bases are equal, the power can be equated.  This gives the number of half-lives that have elapsed as 9 half-lives.

In the problem statement it is given that the time is 3.2 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,

3.2 days   x  (1 half-lifet1/2) = 9 half-lives t1/2 = 3.2 days9 = 0.36day

Therefore, the half-life of the given sample is determined as 0.36 day.

Conclusion

Half-life of the given sample is determined.

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Chapter 11 Solutions

General, Organic, and Biological Chemistry Seventh Edition

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