Magic Numbers

Scientists who study the nuclei of atoms apply the "magic" moniker to elements with a certain number of protons or combinations of protons and neutrons. At the magic numbers of 2, 8, 20, 28, 50, 82 and 126 the protons and neutrons are tightly bound together, giving many "magic" elements a high degree of nuclear stability.

Rutgers scientists have been studying an isotope of tin that is "doubly magic", it contains 50 protons and 82 neutrons. Unlike other magic nuclei that are stable, this isotope of tin is very unstable with a half-life of 40 seconds.

The scientists believe that this isotope of tin may be formed in supernova explosions or collisions of neutron stars, and could be part of the process that forms heavier elements.

Reference:
K. L. Jones, A. S. Adekola, D. W. Bardayan, J. C. Blackmon, K. Y. Chae, K. A. Chipps, J. A. Cizewski, L. Erikson, C. Harlin, R. Hatarik, R. Kapler, R. L. Kozub, J. F. Liang, R. Livesay, Z. Ma, B. H. Moazen, C. D. Nesaraja, F. M. Nunes, S. D. Pain, N. P. Patterson, D. Shapira, J. F. Shriner, M. S. Smith, T. P. Swan, J. S. Thomas. The magic nature of ¹³²Sn explored through the single-particle states of ¹³³Sn. Nature, 2010; 465 (7297): 454 DOI: 10.1038/nature09048

Further Reading
Isotopes
Nuclear Decay
Half-life

Study Questions

1. Explain what is meant by the term isotope.
2. What is the atomic number for the tin isotope described in the article above?
3. What is the mass number for the tin isotope described in the article above?
4. What are the names of the elements that have a nucleus containing the following "magic" numbers of protons:
   
• 2
• 8
• 20
• 28
• 50
• 82
5. Explain what is meant by the term half-life.
6. The half-life of the tin isotope described above is 40 seconds.
   
   • If the original sample had a mass of 0.1g, what mass of tin isotope would be present in the sample after 2 minutes?
   • What percentage of the mass of the original sample would be present after 80 seconds?