Imagine an alternate universe where the value of the Planck constant is 6.62607
ID: 1082166 • Letter: I
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? classical An atom with a mass of 1.0 x 10-27 kg, 178. pm wide, moving at 220. m/s. quantum classical A turtle with a mass of 760. 9, 30. cm long, moving at 2.8 cm/s quantum classical A bacterium with a mass of 2.0 pg, 5.0 m long, moving at 6.00 m/s. quantum classical A mosquito with a mass of 2.2 mg, 12.3 mm long, moving at 2.6 m/s quantumExplanation / Answer
For an atom with a mass 1*10-27 kg, 178pm wide, moving at 220m/s
= h / mv = (6.62607*10-12 Kg m2 / s) / (1*10-27kg*220m/s) = 3.01185*1013 m ( greater than 178 pm)
the atom has width less than the wavelength hence, we can describe this using quantum mechanics.
For a turtle with a mass of 760 gm, 30 cm long moving at 2.8 cm/sec
= (6.62607*10-12 Kg m2 / s) / ( 0.76 Kg * 0.028m/s) = 1.41002*10-13 m = 1.41002*10-15 cm (less than 30cm)
the turtle has more length than the wavelength hence, we can describe this turtle using classical mechanics.
For a bacterium with a mass of 2 pg, 5 m long, moving at 6 m/sec
= (6.62607*10-12 Kg m2 / s) / (2*10-15 kg * 6*10-6 m/s) = 552172500 m = 5.5217*1014 m (greater than 5m)
bacterium's length is higher than the wavelength hence quantum mechanics will best describe the system.
For a mosquito with a mass of 2.2mg, 12.3 mm long, moving at 2.6m/s
= (6.62607*10-12 Kg m2 / s) / ( 2.2*10-3 Kg * 2.6m/s) = 1.1584*10-9 m = 1.1584*10-6mm ( less than 12.3 mm)
Mosquito's length is lower than the wavelength hence classical mechanics will best describe this system.