Question

A magic number is the name given to certain numbers of protons or neutrons that have a high correlation to stability in nuclei:

magic numbers of protons:magic numbers of neutrons:2,8,20,28,50,822,8,20,28,50,82,126,184

A plot of the number of neutrons versus the number of protons for all known stable nuclei, represented by reddish brown dots on the graph, shows that these nuclei cluster together in a region known as the valley of stability. Nuclei with a ratio that is too high tend to undergo beta decay. Nuclei with a ratio that is too low tend to undergo positron emission or electron capture.

Part A

Using general trends, predict the stability of the following nuclei.

Drag the appropriate items to their respective bins, which are Stable and Radioactive

Radium-228, Bromine-82, Sulfur-32,Chlorine-36, Zinc-64

Nuclei with Z≥84 tend to undergo α emission.

Nuclei with high n/p ratios undergo β (  0−1e) emission.

Heavy nuclei with low n/p ratios are more likely to undergo electron (  0−1e) capture.

Light nuclei with low n/p ratios are more likely to undergo positron (01e) emission.

The classification "high" or "low" n/p ratio can be determined by finding the coordinates on the graph that correspond to the number of protons (x or horizontal value) and neutrons (y or vertical value) in a given isotope. Then, observe whether this set of coordinates is above, within, or below the stability valley.
Use this information to solve Part B.

Part B

Using general tendencies and the chart given in the introduction, predict the most likely mode of decay of each of the following radioactive isotopes.

Drag the appropriate items to their respective bins, which are Alpha Decay, Beta Decay, 0/1 e emission, 0/-1 e capture

Iodine-134, Potassium-47,Americium-241,Platinum-183, Fluorine-17

THANK YOU!

Answer 1

So, according to the information given

magic numbers of protons: 2,8,20,28,50,82

magic numbers of neutrons: 2,8,20,28,50,82,126,184

Element	# of protons	#neutrons (atomic mass-#protons)	Ratio # neutrons/# protons	Stability
Radium-228	88	140	1.6	Radioactive (# of protons >83 and high n/p ratio)
Bromine-82	35	47	1.3	Radioactive (high n/p ratio)
Sulfur-32	16	16	1	Stable
Chlorine-36	17	19	1.1	Stable
Zinc-64	30	34	1.1	Stable

To determine the n/p low or high I used the interative tool http://www.nndc.bnl.gov/chart/reCenter.jsp?z=17&n=19 that provides an interactive way to determine it. The atoms matched as stable fall into the stability band.

Element	# of protons	#neutrons (atomic mass-#protons)	Ratio # neutrons/# protons	Decay
Iodine-134	53	81	1.5	Beta decay (n/p large)
Potassium-47	19	28	1.5	Beta decay (n/p large)
Americium-241	95	146	1.5	Alpha decay (Z>83)
Platinum-183	78	105	1.3	electron capture
Fluorine-17	9	8	0.9	0/1 e emission

If you have any doubts please leave a comment :)