Question
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Chapter 11, Problem 11.26EP

(a)

Interpretation Introduction

Interpretation:

If half-life of a radionuclide is 5.0 min, then how much fraction of the radionuclide will be present undecayed after 20 min has to be calculated.

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 11.26EP

Fraction of radionuclide that will remain after 20 min is 1/16.

Explanation of Solution

Half-life of the radionuclide is given as 5.0 min.  The number of half-lives can be calculated as shown below,

20 min   x  (1 half-life5 min) = n half-lives = 4half-lives

The fraction of nuclide that remains after 20 min is calculated as shown below,

(Amountofradionuclideundecayedafternhalflives) =  (Originalamountofradionuclide)  x  (12n) (12n) = 124 = 116

The fraction of sample that remains after 20 min is calculated as 1/16.

Conclusion

The fraction of the radionuclide sample that remains after 20 min is calculated.

(b)

Interpretation Introduction

Interpretation:

If half-life of a radionuclide is 5.0 min, then how much fraction of the radionuclide will be present undecayed after 30 min has to be calculated.

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 11.26EP

Fraction of radionuclide that will remain after 30 min is 1/64.

Explanation of Solution

Half-life of the radionuclide is given as 5.0 min.  The number of half-lives can be calculated as shown below,

30 min   x  (1 half-life5 min) = n half-lives = 6half-lives

The fraction of nuclide that remains after 30 min is calculated as shown below,

(Amountofradionuclideundecayedafternhalflives) =  (Originalamountofradionuclide)  x  (12n) (12n) = 126 = 164

The fraction of sample that remains after 30 min is calculated as 1/64.

Conclusion

The fraction of the radionuclide sample that remains after 30 min is calculated.

(c)

Interpretation Introduction

Interpretation:

If half-life of a radionuclide is 5.0 min, then how much fraction of the radionuclide will be present undecayed after 3 half-lives has to be calculated.

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 11.26EP

Fraction of radionuclide that will remain after 3 half-lives is 1/8.

Explanation of Solution

Given number of half-lives is 3 half-lives.

The fraction of nuclide that remains after 3 half-lives is calculated as shown below,

(Amountofradionuclideundecayedafternhalflives) =  (Originalamountofradionuclide)  x  (12n) (12n) = 123 = 18

The fraction of sample that remains after 3 half-lives is calculated as 1/8.

Conclusion

The fraction of the radionuclide sample that remains after 3 half-lives is calculated.

(d)

Interpretation Introduction

Interpretation:

If half-life of a radionuclide is 5.0 min, then how much fraction of the radionuclide will be present undecayed after 8 half-lives has to be calculated.

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.  Half-life for a radionuclide is constant.

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 11.26EP

Fraction of radionuclide that will remain after 8 half-lives is 1/256.

Explanation of Solution

Given number of half-lives is 8 half-lives.

The fraction of nuclide that remains after 8 half-lives is calculated as shown below,

(Amountofradionuclideundecayedafternhalflives) =  (Originalamountofradionuclide)  x  (12n) (12n) = 128 = 1256

The fraction of sample that remains after 8 half-lives is calculated as 1/256.

Conclusion

The fraction of the radionuclide sample that remains after 8 half-lives is calculated.

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Chapter 11 Solutions

Bundle: General, Organic, and Biological Chemistry, 7th + OWLv2 Quick Prep for General Chemistry, 4 terms (24 months) Printed Access Card

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