Magic Numbers Explained

In nuclear physics, magic numbers refer to the number of nucleons (either protons or neutrons) in an atomic nucleus that are arranged in complete shells. Nuclei with magic numbers of protons or neutrons are significantly more stable and have a higher average binding energy per nucleon compared to nuclei with nearby numbers.

These numbers are analogous to the electron shells in atomic physics which lead to the chemical stability of noble gases. The concept comes from the nuclear shell model.

Identifying Standard Magic Numbers

The experimentally observed and commonly accepted magic numbers for nucleons are:

• 2
• 8
• 20
• 28
• 50
• 82
• 126

Nuclei with both proton and neutron numbers that are magic numbers are called "doubly magic" and are particularly stable (e.g., Helium-4 with 2 protons and 2 neutrons, Oxygen-16 with 8 protons and 8 neutrons, Calcium-48 with 20 protons and 28 neutrons, Lead-208 with 82 protons and 126 neutrons).

Analyzing the Options

We need to examine each given set of numbers to see which one contains only the standard magic numbers listed above.

1. Option 1: 20, 28, 50 and 126

   • 20 is a magic number.
   • 28 is a magic number.
   • 50 is a magic number.
   • 126 is a magic number.

   All numbers in this set are standard magic numbers.

2. Option 2: 24, 28, 82 and 126

   • 24 is not a magic number.
   • 28 is a magic number.
   • 82 is a magic number.
   • 126 is a magic number.

   This set contains a number (24) that is not a magic number.

3. Option 3: 20, 50, 80 and 184

   • 20 is a magic number.
   • 50 is a magic number.
   • 80 is not a standard magic number.
   • 184 is sometimes predicted for superheavy nuclei but is not one of the commonly accepted standard magic numbers from experimental data up to Z=126.

   This set contains numbers (80, 184) that are not standard magic numbers.

4. Option 4: 28, 50, 82 and 180

   • 28 is a magic number.
   • 50 is a magic number.
   • 82 is a magic number.
   • 180 is not a magic number.

   This set contains a number (180) that is not a magic number.

Conclusion

Based on the analysis, only the set in Option 1 consists entirely of the standard magic numbers of nucleons (20, 28, 50, and 126).