A magic number is the name given to certain numbers of protons or neutrons that have a high correlation to stability in nuclei.
Magic # of protons: 2,8,20,28,50,82
Magic # of neutrons: 2,8,20,38,50,82,126, 184
Using general trends, predict the stability of the following nuclei.
Either STABLE or RADIOACTIVE
A)arsenic-82
B)calcium-40
C)radium-233
D)potassium-44
E)zinc-64
(I figured B would be stable because it falls under the magic numbers list. Also I think C would be radioactive because it does not seem to fit with the others)
just a guess but would all but C be stable?
To predict the stability of the nuclei, we can analyze whether the number of protons or neutrons in each nucleus matches any of the magic numbers listed for stability. Here's how you can determine the stability of each nucleus:
A) Arsenic-82: Since arsenic has 82 protons, which is a magic number, it is predicted to be stable.
B) Calcium-40: As you correctly pointed out, calcium-40 has 20 protons, which is a magic number. Therefore, it is predicted to be stable.
C) Radium-233: Radium-233 has 88 protons, which is not a magic number. Similarly, it has 233 neutrons, which is also not a magic number. Based on this analysis, it is more likely to be radioactive rather than stable.
D) Potassium-44: Potassium-44 has 19 protons and 25 neutrons, neither of which match the magic numbers for stability. Therefore, it is more likely to be radioactive.
E) Zinc-64: Zinc-64 has 30 protons, which is not a magic number. However, it has 34 neutrons, which is a magic number. This indicates that it could be stable since one of the magic numbers is satisfied.
Based on this analysis, the predicted stability of each nucleus is as follows:
A) Arsenic-82: STABLE
B) Calcium-40: STABLE
C) Radium-233: RADIOACTIVE
D) Potassium-44: RADIOACTIVE
E) Zinc-64: POTENTIALLY STABLE
Please note that while the magic numbers provide a general trend for stability, the actual stability of a nucleus depends on various other factors as well.
Let's check each of the given nuclei against the magic numbers of protons and neutrons to predict their stability:
A) Arsenic-82:
- Number of protons (atomic number) = 33 (not a magic number)
- Number of neutrons = 82 - 33 = 49 (not a magic number)
Based on these numbers, Arsenic-82 is not a magic number for either protons or neutrons. Therefore, it is predicted to be RADIOACTIVE.
B) Calcium-40:
- Number of protons (atomic number) = 20 (a magic number)
- Number of neutrons = 40 - 20 = 20 (a magic number)
Based on these numbers, Calcium-40 is a magic number for both protons and neutrons. Therefore, it is predicted to be STABLE.
C) Radium-233:
- Number of protons (atomic number) = 88 (not a magic number)
- Number of neutrons = 233 - 88 = 145 (not a magic number)
Based on these numbers, Radium-233 is not a magic number for either protons or neutrons. Therefore, it is predicted to be RADIOACTIVE.
D) Potassium-44:
- Number of protons (atomic number) = 19 (not a magic number)
- Number of neutrons = 44 - 19 = 25 (not a magic number)
Based on these numbers, Potassium-44 is not a magic number for either protons or neutrons. Therefore, it is predicted to be RADIOACTIVE.
E) Zinc-64:
- Number of protons (atomic number) = 30 (not a magic number)
- Number of neutrons = 64 - 30 = 34 (not a magic number)
Based on these numbers, Zinc-64 is not a magic number for either protons or neutrons. Therefore, it is predicted to be RADIOACTIVE.
To summarize:
A) Arsenic-82: RADIOACTIVE
B) Calcium-40: STABLE
C) Radium-233: RADIOACTIVE
D) Potassium-44: RADIOACTIVE
E) Zinc-64: RADIOACTIVE