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Chapter 38: Problem 8

On an energy-release-per-unit-mass basis, by approximately what factor do nuclear reactions exceed chemical reactions?

Short Answer

Expert verified
The nuclear reactions exceed chemical reactions approximately by a factor of \(7.6 \times 10^{7}\).

Step by step solution

01

Understand the Energy Involved in Chemical and Nuclear Reactions

Firstly, it's essential to know that the energy released by reactions involving atomic nuclei (nuclear reactions) is of much higher order compared to that involving electrons (chemical reactions). This difference in energies arises due to the types of forces involved in both kinds of reactions. In nuclear reactions, the strong nuclear force - which is much stronger than the electromagnetic force, is manipulated, leading to the release of high amounts of energy.
02

Calculation of Energy Released in Chemical Reactions

Chemical reactions usually involve bond-breaking and bond-making, and release energy in the range of electron volts (eV). The energy of chemical reactions is around 1 eV per event which is roughly equal to \(4.2 \times 10^{-19}\) joules.
03

Calculation of Energy Released in Nuclear Reactions

In nuclear reactions, energies are usually in the range of Million (MeV) to Billion electron volts (GeV). Taking a simple nuclear reaction such as fusion or fission, the energy released is nearly 200 MeV per event. This is roughly equal to \(3.2 \times 10^{-11}\) joules.
04

Derive the ratio

To find out by how much factor nuclear reactions exceed chemical reactions, divide the energy released by nuclear reactions by the energy released by chemical reactions. The calculation is as follows: \((3.2 \times 10^{-11}\) joules)/(\(4.2 \times 10^{-19}\) joules) which equals approximately \(7.6 \times 10^{7}\).

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