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? A bacterium with a mass of 8.0 p. 5.0 um long, moving at 1.00 m/s. classical O quantum A human with a mass of 59. kg, 2.0 m high, moving at 2.8 m/s. classical O quantum classical A mosquito with a mass of 1.0 mg, 9.7 mm long, moving M 1.6 m/s quantum A buckyball with a mass of 1.2 x 10-21.0.7 nm wide, moving at 24. m/s. classical O quantum X 5 ?

Answer 1

Quantum mechanics

It describes about the motion and correspondence principle, wave particle duality, uncertainty principle, adding the quantization of energy concepts, cooperation of subatomic particles.

Classical Mechanics

In the absence of quantum mechanics it classical mechanics describes the behavior of particles on the basis of Newton's law.

1. A bacterium with the mass of 8 pg, 5$\mu$m long and moving at 1$\mu$m/s

for calculation

  $\lambda$ = h /mu

  $\lambda$ = Planck's Constant

m = mass in Kg

u = speed (m / s)

so, $\lambda$ = 6.62607 * 10 ^-36 J/s / 8 * 10^-9 kg * 0.1 * 10^-5   

= 8.28 * 10 ^-12m

Whereas $\lambda$ value is much more greater than the size of the bacteria it requires Quantum mechanics.

2. A human with the mass of 59kg, 2m high, moving at 2.8 m/s.

$\lambda$ = 6.62607 * 10^-36 J/s / 59kg * 2.8 m/s

= 4.01 *10 ^-34m

Likewise in the before $\lambda$ value is less than the human movement it requires classical mechanics.

3. Mosquito with a mass of 1.0 mg, 9.77 mm long, moving at 1.6 m/s

$\lambda$ = 6.62607 * 10^-36 J/s / 0.1 *10-5 kg * 1.6 m/s

= 4.1 * 10 ^-37 m

$\lambda$ value is lesser than the mosquito movement it require classical mechanics.

4. A buckyball with a mass of 1.2 * 10-21g , 0.7nm wide moving at 24 m/s

$\lambda$ = 6.62607 * 10^-36 J/s / 0.1 *10^-19 kg * 24 m/s

= 1.6 * 10^-56 m

$\lambda$ value is larger than the buckyball movement it require quantum mechanics.