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Chapter 18: Problem 15

What is the relationship between mass defect and binding energy?

Short Answer

Expert verified
The mass defect and the binding energy are directly related through Einstein's equation \(E=mc^2\). The binding energy of the nucleus is the energy equivalent of the mass defect.

Step by step solution

01

Description of Mass Defect

Mass defect refers to the difference between the mass of an atomic nucleus and the sum of the masses of its individual protons and neutrons. It arises because some mass is converted into energy to hold the nucleus together.
02

Definition of Binding Energy

Binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons. It is equivalent to the energy that was released when the nucleus was formed.
03

Relation between Mass Defect and Binding Energy

The conversion of mass into energy is described by Einstein's famous formula \(E=mc^2\), where \(E\) stands for energy, \(m\) for mass, and \(c\) for the speed of light. Applying this formula, the mass defect \(Δm\) can be converted into the binding energy \(E_b\) for the nucleus: \(E_b = Δm c^2\). This means the mass that's 'missing' (the mass defect) has been converted into energy (the binding energy) that holds the nucleus together.

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Most popular questions from this chapter

Determine whether each of the following nuclear reactions involves alpha decay, beta decay, positron emission, or electron capture. \begin{equation}\begin{array}{l}{\text { a. }_{90}^{234} \mathrm{Th} \rightarrow_{-1}^{0} e+_{91}^{234} \mathrm{Pa}} \\ {\text { b. }_{92}^{238} \mathrm{U} \longrightarrow_{2}^{4} \mathrm{He}+_{90}^{234} \mathrm{Th}} \\\ {\text { c. }_{8}^{15} \mathrm{O} \longrightarrow_{+1}^{0} e+_{7}^{15} \mathrm{N}}\end{array}\end{equation}

The energy released by the formation of a nucleus of \(_{26}^{56} \mathrm{U}\) is \(7.89 \times 10^{-11} \mathrm{J}\) Einstein's equation, \(E=m c^{2},\) to determine how much mass is lost (in kilograms) in this process.

Calculate that half-life of cesium-135 if seven-eighths of a sample decays in \(6 \times 10^{6} \mathrm{y}\) .

What is a nucleon?

The half-life of cobalt--60 is 10.47 min. How many milligrams of \(\mathrm{Co}-60\) remain after 104.7 min if you start with 10.0 \(\mathrm{mg}\) of \(\mathrm{Co}-60\) ?
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