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Initial Amount After Half-life (years) Isotope Оuantity 1000 Years 33. 226RA 1599 10 g 94. e 5715 6.58 35. Pu 24,100 2.1g 36. 226Ra 1599 2 g

Initial Amount After Half-life (years) Isotope Оuantity 1000 Years 33. 226RA 1599 10 g 94. e 5715 6.58 35. Pu 24,100 2.1g 36. 226Ra 1599 2 g

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Please do number 36.

(The answer is 3.09g. Please show me the work.)

Thank you!

### Isotope Half-Life Data This table provides information for various isotopes, detailing their half-lives, initial quantities, and amounts remaining after 1000 years. | Isotope | Half-life (years) | Initial Quantity | Amount After 1000 Years | |---------|-------------------|------------------|-------------------------| | \( ^{226}Ra \) | 1599 | 10 g | 2 g | | \( ^{14}C \) | 5715 | 6.5 g | 5 g | | \( ^{239}Pu \) | 24,100 | 2.1 g | 0.4 g | ### Explanation - **Half-life**: The time required for half of the isotope to decay. - **Initial Quantity**: The starting amount of the isotope in grams. - **Amount After 1000 Years**: The remaining quantity of the isotope after 1000 years, also in grams. The table shows how different isotopes decay at varying rates, reflected in the different amounts remaining after the same time period.
Transcribed Image Text:### Isotope Half-Life Data This table provides information for various isotopes, detailing their half-lives, initial quantities, and amounts remaining after 1000 years. | Isotope | Half-life (years) | Initial Quantity | Amount After 1000 Years | |---------|-------------------|------------------|-------------------------| | \( ^{226}Ra \) | 1599 | 10 g | 2 g | | \( ^{14}C \) | 5715 | 6.5 g | 5 g | | \( ^{239}Pu \) | 24,100 | 2.1 g | 0.4 g | ### Explanation - **Half-life**: The time required for half of the isotope to decay. - **Initial Quantity**: The starting amount of the isotope in grams. - **Amount After 1000 Years**: The remaining quantity of the isotope after 1000 years, also in grams. The table shows how different isotopes decay at varying rates, reflected in the different amounts remaining after the same time period.
Expert Solution
Step 1 radioactivity

in radioactivity is defined as unstable nuclei is decay into stable nuclei and emits electromagnetic rays ,

Step 2 calculation

reaction between half life and= decay amount 

A = A° (1/2)n

n = no. Of half life = t / t1/2

A° = initial amount 

amount after 1000 years = 2g 

t1/2 = 1599 years,  

n = 1000/1599 = 0.625

2 = A° (1/2)0.625

 

 

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