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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

What is the density of a solid'? Although the mass densities of solids vary greatly, the number densities (in mol/m3) vary surprisingly little. The value. of course, hinges on the separation between the atoms-but where does a theoretical prediction start? The electron in hydrogen must not as a particle orbiting at a strict radius, as in the Bohr atom. but as a diffuse orbiting wave. Given a diffuse probability, identically repeated experiments dedicated to "finding" the electron would obtain a range of values - with a mean and standard deviation (uncertainty). Nevertheless, the allowed radii predicted by the Bohr model are very close to the true mean values.

(a) Assuming that atoms are packed into a solid typically jBohr radii apart, what would be the number of moles per cubic meter?

(b) Compare this with the typical mole density in a solid of105mol/m3. What would be the value of j?

Electrons are accelerated through a 20 V potential difference producing a monoenergetic beam. This is directed at a double-slit apparatus of 0.010 mm slit separation. A bank of electron detectors is 10 m beyond the double slit. With slit 1 alone open, 100 electrons per second are detected at all detectors. With slit 2 alone open, 900 electrons per second are detected at all detectors. Now both slits are open.

(a) The first minimum in the electron count occurs at detector X. How far is it from the center of the interference pattern?

(b) How many electrons per second will be detected at the center detector?

(c) How many electrons per second will be detected at detector X?

Question: An electron beam strikes a barrier with a single narrow slit, and the electron flux number of electrons per unit time per unit area detected at the very center of the resulting intensity pattern is . Next, two more identical slits are opened, equidistant on either side of the first and equally “illuminated” by the beam. What will be the flux at the very center now? Does your answer imply that more than three times as many electrons pass through three slits than through one? Why or why not?

A particle is connected to a spring and undergoes one-dimensional motion.

(a) Write an expression for the total (kinetic plus potential) energy of the particle in terms of its position x. its mass m, its momentum p, and the force constantof the spring.

(b) Now treat the particle as a wave. Assume that the product of the uncertainties in position and momentum is governed by an uncertainty relationp.r12h. Also assume that because xis on average. the uncertaintyis roughly equal to a typical value of|x|. Similarly, assume thatp|p|. Eliminate pin favor of xin the energy expression.

(c) Find the minimum possible energy for the wave.

The p0 is a subatomic particle of fleeting existence. Data tables don't usually quote its lifetime. Rather, they quote a "width," meaning energy uncertainty, of about 150MeV. Roughly what is its lifetime?

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