Glencoe Chemistry: Matter and Change, Student Edition
Glencoe Chemistry: Matter and Change, Student Edition
1st Edition
ISBN: 9780076774609
Author: McGraw-Hill Education
Publisher: MCGRAW-HILL HIGHER EDUCATION
Expert Solution & Answer
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Chapter EH, Problem 20R
Solution

Interpretation : The amount of sample of the radium-226 left is to be calculated.

Concept Introduction : The chemical element radium has the symbol Ra . The only radioactive member of the group of alkaline earth metals, radium is the hardest known alkaline earth metal. The formula to calculate the amounts of radioactive elements N

is given as:

  N=No12n

Where No is the initial amount, n is the number of half-lives passed.

The leftover sample of radium-226 is 15.625g .

Given information:

The initial amount of sample is 500g .

The elapsed time is 1800 years .

The half-life is 1600 years .

Explanation:

The ratio of elapsed time to the half-life is given as:

  n=tT

Where t is the elapsed time and T is the half-life.

To calculate the ratio of elapsed time to the half-life, substitute the values in the above formula:

  n=tT=1800 years1600 yearsn=5

The formula to calculate the amounts of radioactive elements N

is given as:

  N=No12n

Where No is the initial amount, n is the number of half-lives passed.

To calculate the amount of radioactive element, substitute the values in the above formula:

  N=No12nN=500125=500132N=15.625g

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