Question

Imagine an alternate universe where the value of the Planck constant is

×6.62607·106Js

.

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? An eyelash mite with a mass of 15.7 µg, 240 µm wide, moving at 48. µm/s. classical quantum A raindrop with a mass of 7.0 mg, 7.5 mm wide, moving at 8.4 m/s. classical quantum A paper airplane with a mass of 4.7 g, 210. mm long, moving at 2.3 m/s. classical quantum A car with a mass of 1400. kg, 4.0 m long, moving at 135.0 km/h. classical quantum

Answer 1

h = 6.62607X100 IS a) For eyelash mite, m- 15.7pg = 15.7X10 kg v2 48pm/s = 488106 m/s - Wor= 6.626078 106 IS. 15.7x109 kg x 48 X 10 m/s 18.7981018 m It is too lange to neglect. So, quantum mechanics applies. 6) for rain drop, m= Tong = 7X10 kg v=8.4 m/s x = 6.62607X106 IS [1.128 x 10 m 7x10-6 kg x 8.4 m/s A is too longe, So, quantum mechanics. Paper I c) Airplane, m = 4.7g, v= 2.3m/s 72 6.62607X10 TS 16.13x10 m. 4.78103 kg x 2.3m/s

d) A car

m = 1400 kg

v = 135 km/h = 135 km/h *(1000 m/km)/(3600 s/hr)

= 37.5 m/s

Wavelength = (6.62607 x 10⁶ J•s)/(1400 kg)(37.5 m/s)

= 1.26 m

As the de-Broglie wavelength for all the objects is in observable range. So, all these a) to d) will follow quantum mechanics in alternate universe.