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?

Explanation:

h = 6.62607*10^9 Js

then you will need to apply the debroglie equation

The Equation is given by

λ= h/(mv)

where

λ= Wavelength

h = Planck Constant = 6.62607*10^9 Js (asjusted)

m = mass in kg

v = velocity in m/s

Now, substitute all data

a)

bacteria

8 pg = 8*10^-15 kg

WL = ( 6.62607*10^9) /((8*10^-15)(9*10^-6))

WL = 9.20*10^28

this will be classical

B)

WL = ( 6.62607*10^9) /((39)(2.7))

WL = 62925641.0256 m

classical

c)

m = 1.2*10^-21 g = 1.2*10^-24 kg

v = 22 m/s

WL = ( 6.62607*10^9) /((1.2*10^-24)(22))

WL = 2.50*10^32 m

this will be classical

d)

m = 255 mg = 255*10^-6 kg

v = 8*10^-3 m/s

WL = ( 6.62607*10^9) /((255*10^-6)(8*10^-3))

WL= 3.24*10^15 m

this must be classical

Conclusion

as far as the planet constant decreases; most of phenomena will be modelled and structured with classical equations.

dynamic equilibrium is the answer.