Question

Imagine an alternate universe where the value of the Planck constant is 6.62607 x 10 J.s. | 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? object quantum or classical? O classical A car with a mass of 2000. kg, 4.4 m long, moving at 140.0 km/h. O quantum O classical A virus with a mass of 4.6 x 10-17 g, 410. nm wide, moving at 0.70 pm/s. O quantum classical An atom with a mass of 1.0 x 10-26 kg, 146. pm wide, moving at 236. m/s. O quantum o classical A mosquito with a mass of 2.5 mg, 7.0 mm long, moving at 3.2 m/s. O quantum

Answer 1

$\lambda$ = h/p

$\lambda$(car) = 6.62607×10^-38/(2000×140×1000/3600)

= 8.52×10^-43 m ( the wavelength is negligible compared to dimensions of car . Hence the object can be adequately described by classical mechanics ) Answer: classical

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$\lambda$(virus) = 6.62607×10^-38/(4.6×10^-17×10^-3 × 0.70×10^-6) = 2.06×10^-12 m = 0.0021nm ( wavelength is very small compared to dimension to virus ) . Hence classical mechanics can explain it's behavior . Answer: classical

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$\lambda$(atom) = 6.62607×10^-38/(1.0×10^-26×236) = 2.81×10^-14 m = 2.81 pm ( wavelength is not negligible compared to size of atom, quantum mechanics is required .) Answer: quantum

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$\lambda$(mosquito) = 6.62607×10^-38/(2.5×10^-6×3.2) = 8.28×10^-33 m

Wavelength is neglible compared to its size . Hence classical mechanics can explain it's behavior .

Answer: classical