Question

1. what is a half - life? 21. how much of a 64 mg sample of i - 123 is left after 39 hours if the half - life of i - 123 is 13 hours? 22. what percentage of a sample hassium - 280 will remain after 6 half - lives?

Explanation:

Question 20

A half - life is the time required for half of the atoms of a radioactive substance to decay. It is a characteristic property of each radioactive isotope and is used to describe the rate of radioactive decay.

Step1: Calculate the number of half - lives

The half - life of I - 123 is $t_{1/2}=13$ hours and the time elapsed $t = 39$ hours. The number of half - lives $n=\frac{t}{t_{1/2}}=\frac{39}{13}=3$.

Step2: Use the radioactive decay formula

The amount of a radioactive substance remaining $N$ after $n$ half - lives, given an initial amount $N_0$, is $N = N_0\times(\frac{1}{2})^n$. Here, $N_0 = 64$ mg and $n = 3$. So $N=64\times(\frac{1}{2})^3$.

Step3: Calculate the remaining amount

$N = 64\times\frac{1}{8}=8$ mg.

Step1: Use the radioactive decay formula for percentage

The amount of a radioactive substance remaining $N$ after $n$ half - lives, given an initial amount $N_0$, is $N = N_0\times(\frac{1}{2})^n$. To find the percentage, we calculate $\frac{N}{N_0}\times100\%$. After $n = 6$ half - lives, $\frac{N}{N_0}\times100\%=(\frac{1}{2})^6\times100\%$.

Step2: Calculate the percentage

$(\frac{1}{2})^6=\frac{1}{64}$, and $\frac{1}{64}\times100\% = 1.5625\%$.

Answer:

The time required for half of the atoms of a radioactive substance to decay.

Question 21