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Chapter 21: Problem 11

How does Einstein's equation, \(E=m c^{2},\) enable us to calculate nuclear binding energy?

Short Answer

Expert verified
Einstein's equation, \(E=mc^{2}\), is used to calculate nuclear binding energy by substituting the mass defect of a nucleus (the difference between the total mass of the neutrons and protons and the mass of the nucleus) into the formula. The resulting energy value, typically in Joules, is converted to electron volts.

Step by step solution

01

Understand Einstein's equation

Einstein's equation states that energy (\(E\)) is equal to mass (\(m\)) times the speed of light (\(c\)) squared (\(c^{2}\)). The equation implies that mass and energy are interchangeable.
02

Understand nuclear binding energy

Nuclear binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons. This energy can be calculated based on differences in the mass of the nucleus and its constituents.
03

Apply Einstein’s equation

To calculate the nuclear binding energy, one needs to know the mass of the nucleus (\(m_{nucleus}\)), and the sum of the individual neutrons and protons (\(m_{sum}\)). The mass defect (\(Δm\)) is determined by subtracting the mass of the nucleus from the mass sum (\(Δm = m_{sum} - m_{nucleus}\)). Then by using Einstein’s equation (\(E=mc^{2}\)), we substitute the mass defect into the formula to get the nuclear binding energy.
04

Conversion to appropriate energy unit

The result obtained from step 3 is usually in Joules (J). However, in nuclear physics, binding energy is often expressed in electron volts (eV). Hence, the energy obtained in Joules should be converted to electron volts using the conversion factor \(1 eV = 1.6 \times 10^{-19} J\).

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Most popular questions from this chapter

Both barium (Ba) and radium (Ra) are members of Group \(2 \mathrm{~A}\) and are expected to exhibit similar chemical properties. However, \(\mathrm{Ra}\) is not found in barium ores. Instead, it is found in uranium ores. Explain.

Name two advantages of a nuclear-powered submarine over a conventional submarine.

What is the difference between radioactive decay and nuclear transmutation?

Write an essay on the pros and cons of nuclear power (based on nuclear fission), paying particular attention to its effect on global warming, nuclear reactor safety and weapon risks, and nuclear waste disposal.

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