# 29.8 The particle-wave duality reviewed

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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] .)

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 $\lambda =h/p$ . 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, $p=h/\lambda$ . 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] .)

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:

what is a kaleidoscope?
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.
Onye
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 ?
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....
Abdullateef
what is drift velocity?
avg velocity of a particle in a material due to electric field
Cristiano
what's are maxwells equation on free space??
what is Boltzmann's constant
what is gravitational field strength
Michael
yes ahmed becz a body though with constant speed changes its direction posseses aceleration.
what is Boltzmann constant
Is a body moving with constant speed in a circular path undergoing acceleration?
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
Orji
pls what are the formulas for transformers??
Data's.... yes you could write "a" as "g" provided the term used in the question is "acceleration due to gravity"
Second law of motion
Second law of motion States that the rates of change of momentum is proportional to the external unbalanced force... I.e... : F = ma
Abdullateef
Rheostat is used to control current by varying resistance
I little can't understand this can anyone explain it to me.
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
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)
Data's
rearrange the formula at the beginning and you will get t = (V final - V initial) / a. That is -8 / -10
Data's
you could write "a" as "g"
Data's
(170-L1)÷[L1×(35-10)]=5.5 assume marbles expansion is 5.5