Lab: Half-Life Assignment: Reflect on the Lab

Which equation below BEST describes how many radioactive nuclei remain after n half-life cycles, starting from A initial radioactive atoms? A x .5^n 0.5^n/A 0.5^n A + 0.5^n

A x 0.5^n

You've found some fossil bones while digging in your backyard. Could they be dinosaur bones? Using carbon dating, you determine that 3% of the original radioactive carbon-14 is still radioactive. (The rest has decayed into nitrogen-14.) How many half-life cycles has it gone through? Approximately ? half-life cycles. The half-life of Carbon-14 is 5730 years. When did the animal die? Approximately ? years ago.

5 28,650

The numbers you computed out of 100 could be interpreted as percentages. For example, after four half-life cycles, what percent of radioactive atoms will remain? Now try a real-world example with more than 100 atoms. Start with 5.4 × 1012 radioactive nuclei of Lincolnium. Approximately how many nuclei would still be radioactive after four half-life cycles? 6.750 x 10^11 3.375 x 10^11 1.687 x 10^11

6.25% 3.375 x 10^11

The graph provided shows the accumulation of nonradioactive atoms during the decay of a radioactive substance. Which color graph represents the relationship between the number of half-life cycles and the number (out of 100 nonradioactive atoms) present in a radioactive sample that decays?

Blue

Suppose you could watch radioactive atoms decay. It would probably get quite boring as time went by. Why? Check all that apply. The initial decay rate is very fast, but the decay rate decreases over time. Due to randomness, the last couple of radioactive atoms may take a long time before they become nonradioactive. The pattern becomes very predictable. Only a few radioactive nuclei are left to decay, so fewer and fewer atoms decay. The rate of the decay decreases with each half-life cycle. The probability that an atom will decay is reduced with each half-life cycle.

The initial decay rate is very fast, but the decay rate decreases over time. Due to randomness, the last couple of radioactive atoms may take a long time before they become nonradioactive. The pattern becomes very predictable. Only a few radioactive nuclei are left to decay, so fewer and fewer atoms decay. The rate of the decay decreases with each half-life cycle.

In nuclear medicine, a radioactive isotope, or tracer, can target a particular organ to take a "picture" of it. Which properties of the tracer make it useful in nuclear medicine? Check all that apply. The isotope should have a short half-life. The half-life of the tracer should be long in duration. The tracer should have the ability to damage tissues.

The isotope should have a short half-life. The tracer should have the ability to damage tissues.

The graph provided shows the accumulation of nonradioactive atoms during the decay of a radioactive substance. Why does the correct graph approach the horizontal line at y = 100? Check all that apply. The total number of atoms is 100. The number of half-life cycles it takes for all the nuclei to decay is 100. The final number of nuclei that can decay is 100.

The total number of atoms is 100. The final number of nuclei that can decay is 100.

You could also graph decay time (in seconds or minutes) vs. number of radioactive nuclei. How would this graph differ from the graph of cycle number vs. number of radioactive nuclei? Check all that apply. The graph would flip over. The graph would be logarithmic instead of exponential. The x-axis would change title and values. The y-axis would change title and values.

The x-axis would change title and values.

What is the relationship between the number of half-life cycles and the elapsed time in seconds or minutes? They are the same quantity. They are proportional to each other. They are inversely proportional to each other. They are not related to each other.

They are proportional to each other.

For the graph shown right, a good title for the x-axis is... . A good title for the y-axis is .... The hypothesis stated that the fraction of nuclei still radioactive after n half-life cycles should be 0.5n. How well does the regression equation support the hypothesis? Why is the regression equation not exactly y = 100 • 0.5n?

Time(Half-Life Cycles) Radioactive atoms quite strongly (anyone is fine) Radioactive decay is a random event

After each half-life cycle,... of the radioactive nuclei became nonradioactive. During the experiment, the number of radioactive atoms never increased because a radioactive nucleus.... becomes radioactive again after it decays. Your simulation involved 100 atoms and eight half-life cycles. For half-life cycles 9 and later, how many radioactive nuclei would you expect to be present?

half never 0