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
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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