Imagine an alternate universe where the value of the Planck constant is 6.62607 x 10^6 J-s. In...

Question:

Imagine an alternate universe where the value of the Planck constant is {eq}6.62607 \times 10^6 \;J \cdot s{/eq}. In that universe, which of the following objects would require quantum mechanics to describe, that is, would show both particle and wave properties? Which objects would act like everyday objects and be adequately described by classical mechanics?

a) An alpha particle with a mass of {eq}6.6 \times 10^{-27} {/eq} kg, {eq}8.0 \times 10^{-15} {/eq} m wide, moving at 13.0 km/s.

b) An eyelash mite with a mass of 15.0 μg, 380.0 μm wide, moving at 32.0 μm/s.

c) A ball with a mass of 60 g, 5.1 cm wide, moving at 17.6 m/s.

d) A car with a mass of 1,500 kg, 4.9 m long, moving at 121.0 km/h.

de-Broglie Wavelength:

After the successful confirmation of wave-particle duality by the double-slit experiment, wave-particle duality became an important concept in quantum mechanics. de-Broglie wavelength gives the relation between the wave nature and particle nature of an object.

It is given mathematically as:

{eq}\lambda = \dfrac{h}{p} {/eq}

Where, {eq}\lambda = {/eq} de-Broglie wavelength

h = Planck's constant and

p = momentum of the object

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If in an alternate universe Planck constant is {eq}6.62607 \times 10^6 \;J \cdot s{/eq}, then using the de-Broglie wavelength we can know the wave...