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  • Explain the concept of particle-wave duality, and its scope.

Particle-wave duality —the fact that all particles have wave properties—is one of the cornerstones of quantum mechanics. We first came across it in the treatment of photons, those particles of EM radiation that exhibit both particle and wave properties, but not at the same time. Later it was noted that particles of matter have wave properties as well. The dual properties of particles and waves are found for all particles, whether massless like photons, or having a mass like electrons. (See [link] .)

Part a shows a moving electron represented as a small spherical ball enclosing a wave. An arrow shows the direction of the moving electron. The speed of electron is v. Part b shows a moving photon as a small ellipse enclosing a wave. An arrow shows the direction of the moving photon. The speed of photon is c.
On a quantum-mechanical scale (i.e., very small), particles with and without mass have wave properties. For example, both electrons and photons have wavelengths but also behave as particles.

There are many submicroscopic particles in nature. Most have mass and are expected to act as particles, or the smallest units of matter. All these masses have wave properties, with wavelengths given by the de Broglie relationship λ = h / p size 12{λ = h/p} {} . So, too, do combinations of these particles, such as nuclei, atoms, and molecules. As a combination of masses becomes large, particularly if it is large enough to be called macroscopic, its wave nature becomes difficult to observe. This is consistent with our common experience with matter.

Some particles in nature are massless. We have only treated the photon so far, but all massless entities travel at the speed of light, have a wavelength, and exhibit particle and wave behaviors. They have momentum given by a rearrangement of the de Broglie relationship, p = h / λ size 12{p = h/λ} {} . In large combinations of these massless particles (such large combinations are common only for photons or EM waves), there is mostly wave behavior upon detection, and the particle nature becomes difficult to observe. This is also consistent with experience. (See [link] .)

A massive rock is shown on the left. A massless wave is shown on the right. The propagation of the wave is shown in three dimensional planes, with the variation of two components, E and B. E is a sine wave in one plane with small arrows showing the direction of vibrations. B is a sine wave in a plane perpendicular to the E wave. The B wave has arrows to show the vibrations of particles in the B plane. The waves are shown intersecting each other at the junction of the planes because E and B are perpendicular to each other. The direction of propagation of the wave is shown perpendicular to both E and B waves.
On a classical scale (macroscopic), particles with mass behave as particles and not as waves. Particles without mass act as waves and not as particles.

The particle-wave duality is a universal attribute. It is another connection between matter and energy. Not only has modern physics been able to describe nature for high speeds and small sizes, it has also discovered new connections and symmetries. There is greater unity and symmetry in nature than was known in the classical era—but they were dreamt of. A beautiful poem written by the English poet William Blake some two centuries ago contains the following four lines:

To see the World in a Grain of Sand

And a Heaven in a Wild Flower

Hold Infinity in the palm of your hand

And Eternity in an hour

Integrated concepts

The problem set for this section involves concepts from this chapter and several others. Physics is most interesting when applied to general situations involving more than a narrow set of physical principles. For example, photons have momentum, hence the relevance of Linear Momentum and Collisions . The following topics are involved in some or all of the problems in this section:

Questions & Answers

what is a kaleidoscope?
Egharevba Reply
A kaleidoscope is an optical instrument with two or more reflecting surfaces tilted to each other in an angle, so that one or more (parts of) objects on one end of the mirrors are seen as a regular symmetrical pattern when viewed from the other end, due to repeated reflection. 
well, the reason for the rising of water in capillary tube, Is it the surface tension or adhesive force between water and tube ? Is there any relation of surface tension with adhesive force ? I'm curious to know. Can anyone answer this to me please ?
Aryal Reply
The adhesive force pull the water up the side of the tube.... While the surface tension holds up the water rising in the tube..... and the keep rising until the surface tension balances the weight of water column....
what is drift velocity?
akash Reply
avg velocity of a particle in a material due to electric field
what's are maxwells equation on free space??
what is Boltzmann's constant
Michael Reply
what is gravitational field strength
yes ahmed becz a body though with constant speed changes its direction posseses aceleration.
Ghulam Reply
what is Boltzmann constant
Nweke Reply
Is a body moving with constant speed in a circular path undergoing acceleration?
Ahmad Reply
since it is continually changing its direction I would not say speed but velocity and sinced you said constant then I don't think it is accelerating
pls what are the formulas for transformers??
Salawudeen Reply
Data's.... yes you could write "a" as "g" provided the term used in the question is "acceleration due to gravity"
Victor Reply
Second law of motion
Habeebah Reply
Second law of motion States that the rates of change of momentum is proportional to the external unbalanced force... I.e... : F = ma
Rheostat is used to control current by varying resistance
Jananiy Reply
I little can't understand this can anyone explain it to me.
Samkelisiwe Reply
a ball is kicked with a velocity of 8ms at an angle of 30°to the horizontal. calculate the time of flight of the ball
Galaxy Reply
0.8 seconds. We need vertical speed (y axis) for this task. V final = V initial + a*t. V initial on y axis is 4 m/s, as V initial * sin(30°) = 8 / 2 = 4. Speed of the ball at the start will be equal to its speed when it hits the ground - V final = -4 m/s. a = -10 m/s^2 (acceleration due to gravity)
rearrange the formula at the beginning and you will get t = (V final - V initial) / a. That is -8 / -10
you could write "a" as "g"
(170-L1)÷[L1×(35-10)]=5.5 assume marbles expansion is 5.5
Seyi Reply

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