Chemistry for Today: General, Organic, and Biochemistry
Chemistry for Today: General, Organic, and Biochemistry
9th Edition
ISBN: 9781305960060
Author: Spencer L. Seager, Michael R. Slabaugh, Maren S. Hansen
Publisher: Cengage Learning
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Concept explainers

Question
Chapter 10, Problem 10.51E
Interpretation Introduction

Interpretation:

The mass in grams of the original sample and mass of the sample after 138 days are to be calculated.

Concept introduction:

A radioactive decay series is a series of nuclear reaction in which an unstable radioisotope decays to form a stable isotope.

Nuclear reaction deals with the exchange and release of nucleons and changes the identity of the participating elements.

Expert Solution & Answer
Check Mark

Answer to Problem 10.51E

The mass of the original sample is 0.21g. The mass of the sample after 138 days is 0.208g.

Explanation of Solution

The type of radioactive decay in which an alpha particle is emitted by the nucleus of an atom such that an atom of another element is produced after decay is known as alpha decay. The emission of an alpha particle decreases the atomic number of the parent element by two and atomic mass by four.

The atomic number of Po-210 is 84. Thus, due to alpha decay the atomic number of daughter nuclei is,

=842=82

Similarly, the mass umber changes from 210 to 206. Pb is an element whose atomic number is 84.

Thus, the balanced equation for the decay of Po-210 is as follows:

84210Po24α+82206Pb

It is given that the original sample of Po-210 contains 6.02×1020 atoms.

The formula to calculate number of atoms is,

Numberofatoms=n×NA

Where,

n is the number of moles.

NA is the Avogadro number.

Substitute the given values in the above formula.

Numberofatoms=n×NA6.02×1020=n×6.02×1023n=6.02×10206.02×1023=1×103mol

The formula to calculate number of moles is,

n=mMw

Where,

m is the mass of the substance.

Mw is the molecular weight.

The molecular weight of Po-210 is 210g/mol.

Substitute the value of moles and molar mass in the above formula.

n=mMw1×103mol=m210g/molm=(1×103mol)×(210g/mol)=0.21g

Thus, the mass of the original sample is 0.21g.

The given half-life of Po-210 is 138 days. The half-life period of an element is the amount of time that is required for a radioactive element to get converted to 50% of its initial concentration. Thus, the remaining grams of Po-210 is,

=0.21g2=0.105g

But Pb-206 is also present, thus; the amount Pb-206 is present in the sample is calculated as follows:

AmountofPb-206=0.105gPo×1molPo210gPo×1molPb1molPo×206gPb1molPb=0.103g

The total mass of the sample is calculated as follows:

Totalmass=MassofPo-210+MassofPb-206=0.105g+0.103g=0.208g

Thus, the mass of the sample after 138 days is 0.208g.

Conclusion

The mass of the original sample is 0.21g. The mass of the sample after 138 days is 0.208g.

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Chapter 10 Solutions

Chemistry for Today: General, Organic, and Biochemistry

Ch. 10 - Prob. 10.11ECh. 10 - Prob. 10.12ECh. 10 - Prob. 10.13ECh. 10 - Prob. 10.14ECh. 10 - Prob. 10.15ECh. 10 - Prob. 10.16ECh. 10 - Prob. 10.17ECh. 10 - Prob. 10.18ECh. 10 - Prob. 10.19ECh. 10 - Prob. 10.20ECh. 10 - Prob. 10.21ECh. 10 - Prob. 10.22ECh. 10 - Prob. 10.23ECh. 10 - Prob. 10.24ECh. 10 - Prob. 10.25ECh. 10 - Prob. 10.26ECh. 10 - Prob. 10.27ECh. 10 - Prob. 10.28ECh. 10 - Prob. 10.29ECh. 10 - Prob. 10.30ECh. 10 - Prob. 10.31ECh. 10 - Prob. 10.32ECh. 10 - Prob. 10.33ECh. 10 - Prob. 10.34ECh. 10 - Prob. 10.35ECh. 10 - Prob. 10.36ECh. 10 - Prob. 10.37ECh. 10 - Prob. 10.38ECh. 10 - Prob. 10.39ECh. 10 - Prob. 10.40ECh. 10 - Prob. 10.41ECh. 10 - Prob. 10.42ECh. 10 - Prob. 10.43ECh. 10 - Prob. 10.44ECh. 10 - Prob. 10.45ECh. 10 - Prob. 10.46ECh. 10 - Prob. 10.47ECh. 10 - Prob. 10.48ECh. 10 - Prob. 10.49ECh. 10 - Prob. 10.50ECh. 10 - Prob. 10.51ECh. 10 - Prob. 10.52ECh. 10 - Prob. 10.53ECh. 10 - Prob. 10.54ECh. 10 - Prob. 10.55ECh. 10 - Prob. 10.56ECh. 10 - Prob. 10.57ECh. 10 - Prob. 10.58ECh. 10 - Prob. 10.59ECh. 10 - Prob. 10.60ECh. 10 - Prob. 10.61ECh. 10 - Prob. 10.62ECh. 10 - Prob. 10.63ECh. 10 - Prob. 10.64ECh. 10 - Prob. 10.65ECh. 10 - Prob. 10.66ECh. 10 - Prob. 10.67ECh. 10 - Prob. 10.68ECh. 10 - Prob. 10.69ECh. 10 - Prob. 10.70ECh. 10 - Prob. 10.71ECh. 10 - Prob. 10.72ECh. 10 - Prob. 10.73ECh. 10 - Prob. 10.74ECh. 10 - Prob. 10.75ECh. 10 - Prob. 10.76ECh. 10 - Prob. 10.77ECh. 10 - Prob. 10.78ECh. 10 - Prob. 10.79ECh. 10 - Prob. 10.80ECh. 10 - Prob. 10.81ECh. 10 - Prob. 10.82ECh. 10 - Prob. 10.83ECh. 10 - Prob. 10.84ECh. 10 - Prob. 10.85ECh. 10 - Prob. 10.86E
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