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Chapter 21: Problem 36

The binding energy of an element is \(64 \mathrm{MeV}\). If BE per nucleon is \(6.4\), the number of nucleons are (a) 10 (b) 64 (c) 16 (d) 6

Short Answer

Expert verified
The number of nucleons is 10.

Step by step solution

01

Understanding the Concept

The binding energy (BE) of an element refers to the amount of energy required to disassemble the element into its individual nucleons, which are protons and neutrons. The BE per nucleon is the binding energy divided by the total number of nucleons in the nucleus. We will use this relationship to find the total number of nucleons.
02

Setting up the Equation

You are given that the total binding energy of the element is 64 MeV and the binding energy per nucleon is 6.4 MeV. To find the number of nucleons (let's call this number 'N'), we use the equation: \[ BE = N imes BE_{per\, nucleon} \] where \( BE_{per\, nucleon} = 6.4 \text{ MeV} \) and \( BE = 64 \text{ MeV} \).
03

Solving the Equation

Substitute the given values into the equation: \[ 64 = N imes 6.4 \] Now solve for \( N \) by dividing both sides by 6.4: \[ N = \frac{64}{6.4} \]
04

Calculating the Number of Nucleons

Perform the division: \[ N = \frac{64}{6.4} = 10 \] Thus, the number of nucleons in the element is 10.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Nucleons
Nucleons are the building blocks of the atomic nucleus. These include protons and neutrons.
Protons are positively charged particles, while neutrons have no charge. Despite the difference in charge, both types of particles are roughly equal in mass, and together they create the mass of an atomic nucleus.
In any given nucleus, the sum of protons and neutrons is called the mass number or nucleon number.
  • This reveals the total number of nucleons in the nucleus.
  • The number of protons determines the element's identity on the periodic table.
  • The number of neutrons can vary within atoms of the same element, creating different isotopes.
Every nucleon plays a critical role in the stability and identity of an atom.
Understanding the concept of nucleons is essential for grasping more complex topics in nuclear physics.
Binding Energy per Nucleon
Binding energy per nucleon is a way to measure how tightly each nucleon is held within the nucleus.
It is the total binding energy of the nucleus divided by the number of nucleons.
This value is significant because it gives an insight into the stability of a nucleus. For example:
  • If the binding energy per nucleon is high, it means that the nucleus is more stable.
  • A lower value suggests a less stable nucleus that could be more susceptible to breaking apart.
In the exercise provided, the binding energy per nucleon is 6.4 MeV. This means that, on average, each nucleon contributes 6.4 MeV of binding energy to keep the nucleus intact.
Such calculations help physicists understand nuclear reactions and energy release phenomena.
Nuclear Physics Concepts
Nuclear physics explores the core principles governing atomic nuclei. It's a field that delves into powerful forces and energy levels unique to the subatomic realm.
Key concepts include:
  • Strong Nuclear Force: This force binds nucleons together, overcoming the repulsive electrostatic forces between protons.
  • Radioactivity: Certain nuclei are unstable and release energy by emitting radiation, transforming into different elements.
  • Fission and Fusion: These nuclear reactions involve splitting a heavy nucleus or combining light nuclei, respectively, both releasing copious amounts of energy.
Nuclear physics is crucial for applications ranging from energy production in nuclear reactors to understanding stellar processes.
This field of study not only aids scientific exploration but also has practical benefits in medicine and energy.

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Most popular questions from this chapter

Match the following: List-I (Series) 1\. thorium 2\. naptunium 3\. actinium 4\. uranium List-II (Particles emitted) (i) \(8 \alpha, 5 \beta\) (ii) \(8 \alpha, 6 \beta\) (iii) \(6 \alpha, 4 \beta\) (iv) \(7 \alpha, 4 \beta\) The correct matching is: 1 2 3 4 (a) (iii) (i) (iv) (ii) (b) (i) (ii) (iv) (iii) (c) (iii) (i) (ii) (iv) (d) (ii) (i) (iv) (iii)

If \(5 \mathrm{~g}\) of a radioactive substance has \(\mathrm{t}_{1 / \mathrm{s}}=14 \mathrm{hr}, 10 \mathrm{~g}\) of the same substance will have a \(\mathrm{t}_{1,}\) equal to (a) 14 hours (b) 28 hours (c) 50 hours (d) 70 hours

One of the hazards of nuclear explosion is the generation of \(\mathrm{Sr}^{90}\) and its subsequent incorporation in bones. This nuclide has a half life of \(28.1\) years. Suppose one microgram was absorbed by a new born child, how much \(\mathrm{Sr}^{90}\) will remain in his bones after 20 years? (a) \(61 \mu \mathrm{g}\) (b) \(61 \mathrm{~g}\) (c) \(0.61 \mu \mathrm{g}\) (d) none

A nuclide of an alkaline earth metal undergoes radioactive decay by emission of the \(\alpha\) particle in succession. The group of the periodic table to which the resulting daughter element would belong is (a) Gp 14 (b) Gp 6 (c) Gp 16 (d) Gp 4

Lead is the final product formed by a series of changes in which the rate determining stage is the radioactive decay of uranium-238. This radioactive decay is a first order reaction with a half-life of \(4.5 \times 10^{9}\) years. What would be the age of a rock sample originally lead free, in which the molar proportion of uranium to lead is now \(1: 3\) ? (a) \(1.5 \times 10^{9}\) years (b) \(2.25 \times 10^{9}\) years (c) \(4.5 \times 10^{9}\) years (d) \(9.0 \times 10^{9}\) years
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