Generally speaking, why is the wave nature of matter so counterintuitive?

Short Answer

Expert verified

Because the common dimensions of the world we live in dwarf the wavelength of an electron. Its particle nature is unknown to us; hence a wave nature is unexpected.

Step by step solution

01

The double slit experiment

The double slit experiment is a well-known physics demonstration. It illustrates, with unequalled weirdness, that small atoms and molecules have a wave-like quality to them, and it implies that simply viewing a particle has a huge influence on its functioning.

02

Explanation

Because the wavelength of typical particles is significantly less than the wavelength of an electron, it is highly challenging to witness the wave character of particles in daily life. This is based on the de-Broglie identity which states that λ=hp,where p=mvclassically, because the value of h is so tiny, a small number in the denominator is required to get a wavelength that can be measured.

So, for tiny particles like electrons, a wave-nature will predominate; otherwise, it won't be apparent, and we question their wave-nature.In conclusion, since our perceptions are tied to the dimensions we inhabit—which are substantially larger than those of electrons—we could also anticipate that our conduct will differ.The similar issue emerges with relativity, whose conclusions of time dilation and length contraction are illogical given that we don't often move at or even close to the speed of light.If we had the ability to exist in smaller dimensions or much quicker frames, perhaps all of these occurrences and others would make more sense.

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Most popular questions from this chapter

The top two plots in the accompanying diagram show a Gaussian wave functionψ(x)and its Fourier transformA(k). (a) How does theψ(x)plot demonstrate that the particle’s momentum is roughly(109m-1)h? (b) How does theA(k)plot demonstrate the same thing? (c) If you measured the particle’s momentum,(109m-1)hwould be a likely value. Would(0.9x109m-1)hbe a likely value? Would(1.1x109m1)h? Would(0.5x109m-1)h? (d) The bottom plots show two different Gaussian wave functions. Make sketches of their corresponding Fourier transforms.

The Moon orbits Earth at a radius of 3.84×108m. To do so as a classical particle. Its wavelength should be small. But small relative to what? Being a rough measure of the region where it is confined, the orbit radius is certainly a relevant dimension against which to compare the wavelength. Compare the two. Does the Moon indeed orbit as a classical particle? (localid="1659095974931" mEarth=5.98×1024kgand mmoon=7.35×1022kg)

A beam of particles, each of mass m and (nonrelativistic) speed v, strikes a barrier in which there are two narrow slits and beyond which is a bunk of detectors. With slit 1 alone open, 100 particles are detected per second at all detectors. Now slit 2 is also opened. An interference pattern is noted in which the first minimum. 36 particles per second. Occurs at an angle of 30ofrom the initial direction of motion of the beam.

(a) How far apart are the slits?

(b) How many particles would be detected ( at all detectors) per second with slit 2 alone open?

(c) There are multiple answers to part (b). For each, how many particles would be detected at the center detector with both slits open?

In the hydrogen atom, the electron’s orbit, not necessarily circular, extends to a distance of a about an angstrom (=0.1 nm)from the proton. If it is to move about as a compact classical particle in the region where it is confined, the electron’s wavelength had better always be much smaller than an angstrom. Here we investigate how large might be the electron’s wavelength. If orbiting as a particle, its speed at could be no faster than that for circular orbit at that radius. Why? Find the corresponding wavelength and compare it to . Can the atom be treated classically?

(a) Experiment X is carried out nine times identically, and the value 5is obtained all nine times. Calculate the mean by definition (4-12). Then the standard deviation by definition (4-13). (b) Experiment Yis carried out nine times identically, and the integers 1 through 9 are each obtained once. Repeat the calculations of part (a) for this experiment. (c) For nine repetitions of the experimentZ.The tally is that 1, 5, and 9 are each obtained three times. Repeat the calculations. (d) Explain any differences between the results in parts (b) and (c). Is standard deviation a reasonable measure of spread?

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