Pick the radioactive isotope in each set.
23/11
20/9
Explain your choice.
a)its atomic number is greater than 83
b)it has fewer n than p in the nucleus
c)it is an odd-odd nuclide
none of the above
To determine the radioactive isotope in each set based on the given criteria, let's analyze them one by one:
Set 1: 23/11
a) The atomic number is greater than 83: False
b) It has fewer n than p in the nucleus: False
c) It is an odd-odd nuclide: False
Based on the given criteria, none of the options in Set 1 fit the description. Therefore, none of the isotopes in Set 1 is radioactive.
Set 2: 20/9
a) The atomic number is greater than 83: False
b) It has fewer n than p in the nucleus: True
c) It is an odd-odd nuclide: False
Based on the given criteria, the isotope in Set 2 fits the description of having fewer neutrons than protons in the nucleus. Therefore, the isotope 20/9 in Set 2 is the radioactive isotope.
Summary:
Set 1: None of the isotopes are radioactive.
Set 2: The isotope 20/9 is radioactive because it has fewer neutrons than protons in the nucleus.
To determine the radioactive isotope in each set, let's consider the given criteria.
a) The atomic number is greater than 83: The atomic number represents the number of protons in the nucleus. Since the atomic number of both sets (23 and 20) is less than 83, we can eliminate this choice.
b) It has fewer neutrons than protons in the nucleus: To determine this, we need to find the number of protons (p) and neutrons (n) for each set.
For the first set, 23/11, the atomic number is 11, so it has 11 protons (p). To find the number of neutrons (n), we subtract the atomic number from the mass number, which is 23. Therefore, 23 - 11 = 12 neutrons.
For the second set, 20/9, the atomic number is 9, so it has 9 protons (p). The number of neutrons (n) can be calculated by subtracting the atomic number from the mass number, which is 20. So, 20 - 9 = 11 neutrons.
Comparing the number of neutrons to protons in each set, we see that in the first set, there are fewer neutrons than protons (12 vs. 11). Therefore, the first set (23/11) is the one that satisfies this criterion.
c) It is an odd-odd nuclide: Odd-odd nuclides have both an odd number of protons and an odd number of neutrons. To identify the odd-odd nuclide, we can check whether the atomic number (protons) and the number of neutrons in each set are both odd.
In the first set, 23/11, the atomic number (11) is odd, and the number of neutrons (12) is even, so it does not fulfill this condition.
In the second set, 20/9, the atomic number (9) is odd, and the number of neutrons (11) is also odd. Thus, this set satisfies the odd-odd nuclide criterion.
Based on the analysis, the radioactive isotope in each set is:
- First set (23/11): Does not satisfy criteria a, b, or c.
- Second set (20/9): Satisfies criterion b (fewer neutrons than protons) and criterion c (odd-odd nuclide).