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(a) Which of the following nuclides are magic:122Sn,132Sn,198AU,208pb? (b) Which, if any, are doubly magic?

Short Answer

Expert verified
  1. The nuclides that are magic nuclides:132Sn,98Cd,208Pb
  2. The nuclides that are doubly nuclides: 132Sn,208Pb

Step by step solution

01

The given data:

The given nuclides are 122Sn,132Sn,98Au,208Pb.

02

Understanding the concept of magic numbers:  

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.

03

a) Calculation of the nuclides with magic numbers:

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 132Snis

132-50=82

Whichis a magic number.

Again, the neutron number of 98Cdis,

98-48=50

Which also is a magic number.

Again, the neutron number of 208Pbis,

208-82=126

Which also is a magic number.

Hence as per the concept, the nuclides with the magic numbers are 132Sn,98Cd,208Pb.

04

(b) Calculation of the nuclides with double magic numbers:

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 208Pbis called 鈥渄oubly magic鈥 because they contain both filled shells of protons and filled shells of neutrons.

Thus, the neutron number of 132Snis

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 132Sn,208Pb.

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