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Chapter 34: Problem 13

How might our everyday experience be different if Planck's constant had the value \(1 \mathrm{J} \cdot \mathrm{s} ?\)

Short Answer

Expert verified
If Planck's constant was \(1 \mathrm{J} \cdot \mathrm{s}\), instead of its actual value, the quantum level energy differences would drastically increase. The basic principles of physics would be considerably different. Everyday experiences would be impacted as atomic level interactions could release large amounts of energy, altering many of the processes and interactions we take for granted. Life, as we understand it now, could perhaps be impossible under such conditions.

Step by step solution

01

Understanding Planck's Constant

Planck's constant (\(h\)) is a physical constant that has an actual value of approximately \(6.62607004 × 10^{-34} \mathrm{m}^2 \mathrm{kg} / \mathrm{s}\). It plays a crucial role in the theory of quantum mechanics. The energy \(E\) of a photon is given by \(E=hf\), where \(f\) is the frequency of the photon. Now, if Planck constant were to have a value of \(1 \mathrm{J} \cdot \mathrm{s}\), the energy levels would be significantly larger.
02

Explaining the Consequences

As the energy levels increase due to a massive increase in the value of Planck's constant, it would affect everything from how matter interacts at a subatomic level to the fundamental principles of physics. Studying and predicting physical phenomena would become more complex at this scale. We might experience larger energy differences in atomic transitions resulting in high energy quantum effects being more apparent in the macro world.
03

Impacts on Everyday Life

In everyday life, drastic changes would occur. Since energy levels of atomic and subatomic particles will be much larger, normal interactions in daily life could release massive amounts of energy. Fundamental aspects of life, such as light's interaction with matter, chemical reactions, and the nature of electrical devices, among others, would be extremely different. Possibly, the existence of life under these conditions could potentially be impossible given our current understanding of life's requirements.

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