Chapter 2: Problem 5

Discuss nuclear models in details. What is the concept of magic numbers?

Short Answer

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Nuclear models such as the liquid drop model, shell model and collective model attempt to explain the properties of atomic nuclei. The concept of 'magic numbers' in nuclear physics refers to the specific numbers of nucleons that form complete shells in the atomic nucleus, leading to exceptional stability. These magic numbers are \(2, 8, 20, 28, 50, 82, 126\).

Step by step solution

Introduction to Nuclear Models

Nuclear models are theoretical models that seek to explain the properties of atomic nuclei. These include the liquid drop model, shell model and collective model.

The Liquid Drop Model

The liquid drop model proposes that the nucleus of an atom behaves similarly to a droplet of liquid. This model is used to explain nuclear fission, where a heavy nucleus splits into two lighter ones, and nuclear fusion, where two light nuclei merge to form a heavier one.

The Shell Model

This model suggests that the nucleus is composed of several energy levels, or 'shells'. When these energy levels are full, the nucleus is particularly stable. This model greatly explains the concept of 'magic numbers'.

The Collective Model

This model looks at the collective motion of the nucleons. It is often used to describe certain types of nuclear rotation and vibration.

Introduction to Magic Numbers

Magic numbers in nuclear physics refer to numbers of nucleons (either protons or neutrons) that are arranged into complete shells within the atomic nucleus. The term 'magic number' signifies the extreme stability of such nuclei.

Explanation of magic numbers

The concept is explained in the context of the shell model. Magic numbers are the number of nucleons at which a shell is filled, giving additional stability to the atom. The magic numbers are \(2, 8, 20, 28, 50, 82, 126\).

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Discuss nuclear models in details. What is the concept of magic numbers?

Short Answer

Step by step solution

Introduction to Nuclear Models

The Liquid Drop Model

The Shell Model

The Collective Model

Introduction to Magic Numbers

Explanation of magic numbers

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