O ELECTRONIC STRUCTURE Understanding the meaning of a de Broglie wavelength Imag
ID: 706508 • Letter: O
Question
O ELECTRONIC STRUCTURE Understanding the meaning of a de Broglie wavelength 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? An alpha particle with a mass of 6.6 x 1027 kg, 8.0 x 10 15 m wide, moving at 13. km/s. o quantum O classical O quantum An airplane with a mass of 2.79 x 104 kg, 14.0 m long moving at 1700. km/h. at 2.9 m/'s O quantum A turtle with a mass of 450. g, 20. cm long, moving at 1.s cm/s. O classical O quantumExplanation / Answer
Sol:-
Given
planck constant i.e h = 6.62607 x 109 Js = 6.62607 x 109 kg m2 s-1
Now from de-Broglie equation , we have
?= h / mv ...........(1)
where
?= Wavelength
m = mass (in kg)
v = velocity (in m/s)
(a)
Given , m = 6.6 x 10-27 kg and v = 13 km/s = 13000 m/s
now from equation (1) , we have
?= 6.62607 x 109 kg m2 s-1 / 6.6 x 10-27 kg x 13000m/s
?= 7.72 x 1031 m
classical
(b)
Given , m = 2.79 x 104 kg and v = 1700 km/s = 1700000 m/s
now from equation (1) , we have
?= 6.62607 x 109 kg m2 s-1 / 2.79 x 104 kg x 1700000 m/s
?= 0.1397 m
classical
(c)
Given , m = 1.2 mg = 1.2 x 10-6 kg and v = 2.9 m/s
now from equation (1) , we have
?= 6.62607 x 109 kg m2 s-1 / 1.2 x 10-6? kg x 2.9 m/s
?= 1.9 x 1015 m
classical
(d)
Given , m = 450 g = 0.45 kg and v = 1.5 cm/s = 0.015 m/s
?= 6.62607 x 109 kg m2 s-1 / 0.45 kg x 0.015 m/s
?= 9.82 x 1011 m
classical
Note :- because the value of planck constant decreases therefore all these four are labeled as classical equations.
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