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Radioactive substances follow a specific law of decay. Namely, if you have a sample of some radioactive isotope, the quantity left after a certain time, called the half-life and denoted T1/2, is one-half of what you had initially. If you wait a second half-life, then there will be half of what was left at the end of the first half-life. Since 1/2-1/2 = 1/4, you will have one-fourth of the original quantity left after two half-lives. You can continue with this procedure to find the fraction of the original sample that hasn't decayed after any number of half- lives. However, this would become quite cumbersome if you are interested in the quantity left after, say, 10 half-lives. In this case, the quantity you are looking for would be found by multiplying the original quantity by 10 factors or 1/2. To solve this problem, we use exponents. An exponent, a small number written above and to the right, tells you how many copies of a particular number are multiplied together. In our example, where the original quantity of radioactive isotope must be multiplied by 10 factors of 1/2, you can write the multiplication in a more compact way as 10 (-)¹ Part C Which of the following are equivalent to (1/2)8? Check all that apply. - (-¹) 5 0 □ (²) ² · () ³ · (;)) ³ □ (-)² · (-;-) ³² · () ² Submit Request Answer Part D Complete previous part(s) (-) ² · (-¹)³ = (-¹) ¹¹¹

Radioactive substances follow a specific law of decay. Namely, if you have a sample of some radioactive isotope, the quantity left after a certain time, called the half-life and denoted T1/2, is one-half of what you had initially. If you wait a second half-life, then there will be half of what was left at the end of the first half-life. Since 1/2-1/2 = 1/4, you will have one-fourth of the original quantity left after two half-lives. You can continue with this procedure to find the fraction of the original sample that hasn't decayed after any number of half- lives. However, this would become quite cumbersome if you are interested in the quantity left after, say, 10 half-lives. In this case, the quantity you are looking for would be found by multiplying the original quantity by 10 factors or 1/2. To solve this problem, we use exponents. An exponent, a small number written above and to the right, tells you how many copies of a particular number are multiplied together. In our example, where the original quantity of radioactive isotope must be multiplied by 10 factors of 1/2, you can write the multiplication in a more compact way as 10 (-)¹ Part C Which of the following are equivalent to (1/2)8? Check all that apply. - (-¹) 5 0 □ (²) ² · () ³ · (;)) ³ □ (-)² · (-;-) ³² · () ² Submit Request Answer Part D Complete previous part(s) (-) ² · (-¹)³ = (-¹) ¹¹¹

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Radioactive substances follow a specific law of decay. Namely, if you have a sample of some radioactive isotope, the quantity left after a certain time, called the half-life and denoted T1/2, is one-half of what you had initially. If you wait a second half-life, then there will be half f what was left at the end of the first half-life. Since 1/2-1/2 = 1/4, you will have one-fourth of the original quantity left after two half-lives. You can continue with this procedure to find the fraction of the original sample that hasn't decayed after any number of half- lives. However, this would become quite cumbersome if you are interested in the quantity left after, say, 10 half-lives. In this case, the quantity you are looking for would be found by multiplying the original quantity by 10 factors or 1/2. To solve this problem, we use exponents. An exponent, a small number written above and to the right, tells you how many copies of a particular number are multiplied together. In our example, where the original quantity of radioactive isotope must be multiplied by 10 factors of 1/2, you can write the multiplication in a more compact way as 10 (1) ¹⁰ Part C Which of the following are equivalent to (1/2)³? Check all that apply. - (-/-)5 (-¹) ¹. (-)² □ (-) ² · () ³ · (-) ³ ()² · ()² · () ² Submit Request Answer Part D Complete previous part(s) I+Y (²) ² · ( ¹ )³ = (-²) ¹¹⁹.
Transcribed Image Text:Radioactive substances follow a specific law of decay. Namely, if you have a sample of some radioactive isotope, the quantity left after a certain time, called the half-life and denoted T1/2, is one-half of what you had initially. If you wait a second half-life, then there will be half f what was left at the end of the first half-life. Since 1/2-1/2 = 1/4, you will have one-fourth of the original quantity left after two half-lives. You can continue with this procedure to find the fraction of the original sample that hasn't decayed after any number of half- lives. However, this would become quite cumbersome if you are interested in the quantity left after, say, 10 half-lives. In this case, the quantity you are looking for would be found by multiplying the original quantity by 10 factors or 1/2. To solve this problem, we use exponents. An exponent, a small number written above and to the right, tells you how many copies of a particular number are multiplied together. In our example, where the original quantity of radioactive isotope must be multiplied by 10 factors of 1/2, you can write the multiplication in a more compact way as 10 (1) ¹⁰ Part C Which of the following are equivalent to (1/2)³? Check all that apply. - (-/-)5 (-¹) ¹. (-)² □ (-) ² · () ³ · (-) ³ ()² · ()² · () ² Submit Request Answer Part D Complete previous part(s) I+Y (²) ² · ( ¹ )³ = (-²) ¹¹⁹.
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