Question

l e an alternate universe where the value of the Planck constant is 6.62607x 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? An atom with classical moving at 17 ass of 1.0 x 10 kg, 133. pm wide, m/s. quantum o dassical An iceberg with a mass of 3.4 x 10 kg, 110. m wide. moving at 0-56 km/h quantum paper airplane with a mass of 5.8 g, 235. mm long moving at 3.3 m/s. Odassical O quantum dlassical A raindrop with a mass of 22.0 mg, 2.0 mm wide, moving at 8.5 m/s quantum 2

Answer 1

Hi

We should remember that the wavelength is given by h/p

It we see the wavelength in all cases

Case 1

Wavelength =(6.6*10^-6 )/(1*10^-26*1.75 )= 3.77*10 ^18 m

Case 2

Case 2
Wavelength(6.6*10^-6 )/(3*10^8*(560÷3600))
=1.41 *10^-13 m
Case 3
Wavelength(6.6*10^-6 )/((5.8/1000)*3.3)
=3.44 *10^-4
Case 4
Wavelength(6.6*10^-6 )/(23*10^-6*8.5)
=0.03 m

We can see that in the case 2 we have the wavelength that is quite small to be notice so we can't apply the quantum theory and thus we need to use the classical theory.

In all other case we can use the quantum theory.

Hope this helps
Feel free to comment in the case of any doubt.
Thank you