Final answer:
In an alternate universe with Planck's constant being 6.62607 x 10⁻⁴ J·s, a virus might fall into the quantum realm, while paper and real-sized airplanes, as well as a grain of sand, would likely remain in the classical realm.
Step-by-step explanation:
To answer this question, we first consider the de Broglie wavelength which is relevant when assessing the quantum mechanical versus classical behavior of objects. The de Broglie wavelength λ is given by λ = h/p, where h is Planck's constant and p is the momentum of the object. In an alternate universe where the Planck constant is h = 6.62607 x 10⁻⁴ J·s, much larger than its actual value (6.62607015 x 10⁻³⁴ J·s), quantum effects become noticeable on significantly larger scales.
Using the de Broglie wavelength, we can determine whether the following objects behave in a quantum mechanical way (display wave properties) and when they can be described by classical mechanics:
- A virus with a mass of 1.0x 10¹⁷ g and a velocity of 0.70 µm/s would have a de Broglie wavelength that may fall into the quantum realm and, hence may require quantum mechanics to describe its behavior (Quantum).
- A paper airplane with a mass of 4.4 g moving at 2.9 m/s would likely still act like an everyday object and be adequately described by classical mechanics (Classical).
- An airplane with a mass of 1.40 x 10⁴ kg traveling at 1500 km/h would definitely behave as an everyday object and classical mechanics would suffice (Classical).
- A grain of sand with a mass of 135 mg moving at 10.00 mm/s might start to exhibit quantum properties due to the increase of Planck's constant, but it would likely still be largely within the classical regime (Classical).
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