Question

O ELECTRONIC STRUCTURE Understanding the meaning of a de Broglie wavelength DOOD Falak Imagine an alternate universe where the value of the Planck constant is 6.62607* 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 eyelash mite with a mass of 13.0 . 305 um wide, moving at 26. umys. quantum classical A turtle with a mass of 810. 9. 25. сm long, moving at 2.8 cms. O quantum classical A car with a mass of 2000 kg, 4.7 m long, moving at Inm/h

Answer 1

first of all, in all that case we have to calculate the de-broogli ware length (x) by the following equation - i h h = Planck Const. m xv ma mass in kg [va speed in m/s Then we will compare the calcul- ated wave length value with the size/ length of the given systems. Now, if the a calculated wavele- ngth is much much greater than the given sizes, then we will describe the object by quantum mechanics and if it becomes smalks then we will use classical mecha- nies. 1st object : eyelash mite mass = 13.0 Mg - 13 x 10-8 kg

= 26 umls - 5 = 2.6 x 10 m/s & Here given -12 h = 6.62607 x 10 Jos mxv 6.62607 8 10-12 Jos 7.3 x 10-8 kg x 2.6 x 10 5 m/s = 19.6 m (> 305 um wide) So we can see that the wave- length of the eye-lash mite ie. 19.6 m is greater than the width of 305 um. So, An eyelash mite with a mass of 13.0 Mg , 305 mm wide, mon- ng at 26 mm/s. L o quantum

2nd object : turtle m=810 g = 0.81 kg v=2-8 cm/s = 0.028 m/s de_h x = mv -12 = 6.62607 x 10 J.S. 0-81 kg x 0.028 m/s lona long = 2.9 x 101m 25 cm 2 Thus, - A twitle with a mass of 810 g 25 cm long, moving at 2.8 cm/s L & classical 3rd object : Car m = 2000 kg ; V=128 km/h = 128x1000 m 3600 S = 35.55 m/s

oi = 6.62607 X 10-12 d. s 2000 kg x 35.55 m/s = 9.3x10-17 m (44.7 m) Thus, long A car with a mass of 2000 kg 4.7 m long, moving at 128.0 km/h L o classical 4th object : mosquito m = 2.1 mg = 2-1 x 10-6 kg v=1.4 m/s 6.62607 810-12 d. s 2.18 10-6 kg x 1.4 m/s = 2.25 x 10-6 m k 12 mm Thus, - long ) A mosquito with a mass of 210 12.0mm long moving at 1.4 on/s - o classical. и