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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
Nuclear reactions exceed chemical reactions by a factor of around \(10^6 \).

Step by step solution

01

Define Chemical Reaction Energy Release

In chemical reactions, the energy released per unit mass associated with the breaking and forming of bonds is in the order of electron volts (eV) per atom. This corresponds to approximately 1.6 × 10^-19 J (1 eV = 1.6 × 10^-19 J). Considering an atomic mass unit \( u \) (1 atom of Carbon-12) is about \( 1.66054 × 10^-27 \) kg, the energy per unit mass for chemical reactions can be calculated as approximately \( (1.6 × 10^-19 J)/(1.66054 × 10^-27 kg) ≈ 10^8 \) J kg^-1.
02

Define Nuclear Reaction Energy Release

In nuclear reactions, the energy released per unit mass associated with the transformation of matter is in the order of millions of electron volts (MeV) per atom. This corresponds approximately to \( 1.6 × 10^-13 \) J. Considering an atomic mass unit \( u \) (1 atom of Carbon-12) is about \( 1.66054 × 10^-27 \) kg, the energy per unit mass for nuclear reactions is roughly \( (1.6 × 10^-13 J)/(1.66054 × 10^-27 kg) ≈ 10^14 \) J kg^-1.
03

Compare the Energy Scales

The factor by which nuclear reactions exceed chemical reactions can be obtained by dividing the energy per unit mass for nuclear reactions by that for chemical reactions. Thus, the factor is estimated as \( 10^14 / 10^8 = 10^6 \).

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