It has been found that nuclides with `2,8,20,50,82,` and `126` protons or neutrons are exceptionally stable. These numbers are refferd to as the magic numbers and their existance has led to.

Options

A. the idea of periodictiy in nuclear properties similar to the periodicity of chemical elements in periodic table
B. the so-called ''liquid drop model of the nucleus''
C. the so-called ''shell model of the nuclus''
D. have a conveninet exploanation of ''nuclear fission''

Explanation

To address the question regarding the stability of nuclides with specific numbers of protons or neutrons, known as magic numbers, we can break down the explanation into several steps:

### Step-by-Step Solution:

1. **Understanding Magic Numbers**:
- Magic numbers are specific numbers of protons or neutrons in a nucleus that result in a more stable configuration. The magic numbers identified are 2, 8, 20, 50, 82, and 126.

2. **Stability of Magic Numbers**:
- Nuclides with these magic numbers exhibit exceptional stability due to the complete filling of nuclear shells. This is analogous to the electron configuration in atoms where filled electron shells lead to greater stability.

3. **Nuclear Shell Model**:
- The existence of magic numbers supports the shell model of the nucleus. This model suggests that nucleons (protons and neutrons) occupy discrete energy levels or shells within the nucleus, similar to electrons in an atom.

4. **Binding Energy**:
- The binding energy per nucleon is a crucial factor in understanding stability. For magic numbers, the binding energy per nucleon is higher compared to adjacent numbers of nucleons. This indicates that these configurations are energetically favorable and thus more stable.

5. **Graphical Representation**:
- A graph of binding energy versus the number of nucleons shows peaks at the magic numbers. These peaks correspond to the increased stability and higher binding energy per nucleon for nuclides with magic numbers.

6. **Implications**:
- The existence of magic numbers has led to a better understanding of nuclear properties and behaviors, including the periodicity of nuclear stability, similar to the periodic table of elements in chemistry.

### Final Conclusion:
The discovery of magic numbers has significantly contributed to the development of the nuclear shell model and our understanding of nuclear stability and binding energy.

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