Question

Without using a calculator, enter the correct value of 5-2 Express your answer to three significant figures or as a fraction. Radioactive substanoces 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 71/2 onehalf of what you had initially. If you wait a second hai-ife, 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 muiltiplying the original quantity 5-2 = 4.00x10 V Correct To solve this problem, we use exponents. An exponent, a small number wnitten 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 If you initially had N atoms of some radioactive isotope, then after three half-lives, you would have N (1/2) atoms left. After another two half-lives, you would have N (1/2) (1/2) atoms left Saying "Tirst three, then two more" doesnt affect the fact that you have undergone a total of five half-lives, so equally valid would be to say that at the end of these two periods you have N (L/2) atoms left. Setting the two expressions equal .e, N(1/(1/2)N(/2) mustrates an important rule about exponents: Multiplying the same number to two diflerent exponents is equal to raising that number to the sum of those exponents. After dividing the N out of our example, we see that Of course, s + 2 5, so you can see the rie in erect. Using 1:2 as our base, the rie can be written generally as Part C Which of the following are equivalent to (1/2) Check all that apply. 47-4 Submit

Answer 1

part C)
1st and 3rd options are correct.

because
1st option) (1/2)^3*(1/2)^5 = (1/2)^(3 + 5)

= (1/2)^8

3rd option) (1/2)^2*(1/2)^3*(1/2)^3 = (1/2)^(2+3+3)

= (1/2)^8