Suggested languages for you:

Americas

Europe

Q13Q

Expert-verifiedFound in: Page 1302

Book edition
10th Edition

Author(s)
David Halliday

Pages
1328 pages

ISBN
9781118230718

**(a) Which of the following nuclides are magic:**** ${{\mathbf{}}}^{{\mathbf{122}}}{\mathbf{Sn}}{\mathbf{,}}{\mathbf{}}{{\mathbf{}}}^{{\mathbf{132}}}{\mathbf{Sn}}{\mathbf{,}}{{\mathbf{}}}^{{\mathbf{198}}}{\mathbf{AU}}{\mathbf{,}}{\mathbf{}}{{\mathbf{}}}^{{\mathbf{208}}}{\mathbf{pb}}$**** ****? (b) Which, if any, are doubly magic?**

- The nuclides that are magic nuclides:${}^{132}\mathrm{Sn},{}^{98}\mathrm{Cd},{}^{208}\mathrm{Pb}$
- The nuclides that are doubly nuclides: ${}^{132}\mathrm{Sn},{}^{208}\mathrm{Pb}$

The given nuclides are ${}^{122}\mathrm{Sn},{}^{132}\mathrm{Sn},{}^{98}\mathrm{Au},{}^{208}\mathrm{Pb}$ .

**In nuclear physics, magic numbers are several nucleons such that the nucleons of the nuclide are arranged into complete shells within the atomic nucleus. Thus, their nuclei are more stable than in comparison to other nuclides. They are 2, 8, 20, 28, 50, 82, 126, and so on.**

**In some cases there the isotopes can consist of magic numbers for both protons and neutrons and those are called double magic numbers. They occur at the heavier nuclides. The magic numbers are: 2, 8, 20, 28, 50, 82, and 114.**

Any nuclide whose proton number *Z* or neutron number *N* has one of these values turns out to have a special stability that may be made apparent in a variety of ways are called magic nuclides.

Thus, the neutron number of ${}^{132}\mathrm{Sn}$ is

$132-50=82$

Which is a magic number.

Again, the neutron number of ${}^{98}\mathrm{Cd}$ is,

$98-48=50$

Which also is a magic number.

Again, the neutron number of ${}^{208}\mathrm{Pb}$ is,

$208-82=126$

Which also is a magic number.

Hence as per the concept, the nuclides with the magic numbers are ${}^{132}\mathrm{Sn},{}^{98}\mathrm{Cd},{}^{208}\mathrm{Pb}$ .

Any nuclide whose proton number *Z* and neutron number *N* has both of the values turns out to have a special stability that may be made apparent in a variety of ways are called doubly magic nuclides.

The nuclide ${}^{208}\mathrm{Pb}$ is called “doubly magic” because they contain both filled shells of protons and filled shells of neutrons.

Thus, the neutron number of ${}^{132}\mathrm{Sn}$ is

$132-50=82$

Which is a magic number and also the proton number 50 is magic number.

Hence as per the concept, the nuclides with the double magic numbers are ${}^{132}\mathrm{Sn},{}^{208}\mathrm{Pb}$.

94% of StudySmarter users get better grades.

Sign up for free