Question

activity b: band of stability
get the gizmo ready: • on the graph, make sure the x - axis and y - axis range from 0 - 20. if not, click the o zoom control.
introduction: some atoms are stable, while others are radioactive. in a radioactive atom, the nucleus has the potential to break down, or decay, and change into a different element. for example, radon - 222 is radioactive. when it decays, its nucleus loses enough protons and neutrons to become polonium - 218. radioactive isotopes are also called radioisotopes.
question: how can we predict whether an isotope will be stable or radioactive?

1. observe: use the gizmo to create a carbon - 12 isotope.

a. is this isotope stable or radioactive?

b. add a neutron to create carbon - 13. is this isotope stable or radioactive?

c. add another neutron. is this isotope stable or radioactive?

d. what is the half - life of this isotope?

the half - life of a radioisotope is the time it takes for 50% of the atoms in a sample to decay. the shorter the half - life, the more unstable the nucleus.

1. collect data: set protons to 1 and neutrons to 0. below the graph, click save point. notice on the graph the stable isotopes are shown in blue and the radioactive isotopes in green.

add protons and neutrons and use the save point button to record data for the first seven elements. try to find all of the stable isotopes. (note: you can drag the point direction to any location on the graph.)
a. do the stable isotopes appear to fall on a line?

b. how many stable isotopes have equal numbers of protons and neutrons?

c. turn on show neutron:proton ratio. drag the blue line until it lines up with most of the blue points. approximately what n:p ratio do most stable isotopes have?

1. explore: investigate the different radioactive isotopes you have saved.

a. which radioisotope is most stable, and what is its half - life?

b. in general, how does the half - life change as you move farther away from the stable isotopes?

Explanation:

Step1: Recall carbon - 12 properties

Carbon - 12 has 6 protons and 6 neutrons and is a stable isotope.

Step2: Consider carbon - 13

Carbon - 13 has 6 protons and 7 neutrons and is also stable.

Step3: Consider carbon - 14

Carbon - 14 has 6 protons and 8 neutrons and is radioactive with a half - life of about 5730 years.

Step4: Analyze stable isotopes on graph

Stable isotopes often follow a certain pattern related to the neutron - proton ratio. For light elements, stable isotopes often have a neutron - proton ratio close to 1.

Step5: Analyze stability and half - life

The most stable radioisotope among those considered is the one with the longest half - life. As we move further from stable isotopes, the half - life generally decreases.

Answer:

1.
A. Stable
B. Stable
C. Radioactive
D. Approximately 5730 years
2.
A. Yes
B. For light elements like hydrogen (1 proton, 1 neutron - deuterium), helium (2 protons, 2 neutrons), etc., there are several. The number depends on the elements considered in the first seven elements, but for example, hydrogen (deuterium), helium - 4, carbon - 12, oxygen - 16 are some with equal numbers of protons and neutrons among the first seven elements.
C. For light elements, the neutron - proton ratio of most stable isotopes is close to 1.
3.
A. This depends on the specific radioisotopes saved. But generally, a radioisotope with a longer half - life is more stable. For example, if carbon - 14 is among them, its half - life is 5730 years.
B. The half - life generally decreases as we move further from stable isotopes.