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# Particle or Wave? Help

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## Introduction

The question, “Is an EM field a barrage of particles or a wave disturbance?” has never been fully and rigorously answered. There is a relation, however, between photon energy, frequency, and wavelength.

## Energy, Frequency, And Wavelength

The energy contained in a single photon of EM energy can be found in terms of the frequency by this formula:

e = hf

where e is the energy (in joules) contained in a photon, f is the frequency of the EM wave disturbance (in hertz), and h is a constant known as Planck’s constant , approximately equal to 6.6262 × 10 −34 .

If the wavelength λ (in meters) is known, and c is the propagation speed of the EM disturbance (in meters per second), then

e = hc

This can be rearranged to determine the wavelength of a photon in terms of the energy it contains:

λ = hc/e

For EM rays in free space, the product hc is approximately equal to 1.9865 × 10 −25 because c is approximately equal to 2.99792 × 10 8 m/s.

#### Problem 1

What is the energy contained in a photon of visible light whose wavelength is 550 nm in free space?

#### Solution 1

First, convert 550 nm to meters; 550 nm = 550 × 10 −9 m = 5.50 × 10 −7 m. Then use the formula for energy in terms of wavelength:

e = hc

= (1.9865 × 10 −25 )/(5.50 × 10 −7 )

= 3.61 × 10 −19

#### Problem 2

What is the wavelength of an EM disturbance consisting of photons that all have 1.000 × 10 −25 J of energy in free space?

#### Solution 2

Use the formula for wavelength in terms of energy:

λ = hc/e

= (1.9865 × 10 −25 )/(1.000 × 10 −25 )

= 1.9865 m

This turns out to be a signal in the very-high-frequency (VHF) radio range. You can calculate the exact frequency if you like.

## Double-slit Experiments

If a beam of light gets dim enough, its photons emanate from the source at intervals that can be measured in seconds, minutes, hours, days, or years. If a beam of light gets brilliant enough, its photons rain down at the rate of trillions per second. These particles can be detected and their energy content determined just as if they were tiny bullets traveling at 2.99792 × 10 8 m/s in free space. However, the particle theory of EM radiation does not explain refraction of the sort that occurs at the surface of a body of water. The corpuscular theory also fails to explain beating and interference effects that are observed with visible light and high-speed subatomic particles. The classic double-slit experiment has been used as a demonstration of the wavelike nature of visible light. The following is a somewhat oversimplified description of this experiment.

An English physicist named Thomas Young devised an experiment in the hope of resolving the particle/wave question. He shone a beam of light having a certain color and a nearly perfect point source at a barrier with two narrow slits cut in it. Beyond the barrier was a photographic film. The light would, Young supposed, pass through the two slits and land on the film, producing a pattern. If light is comprised of corpuscles, then the pattern on the film ought to be two bright vertical lines. If light is a train of waves, an interference pattern ought to appear in the form of alternating bright and dark bands. When the experiment was carried out, the verdict was clear: Light is a wave disturbance. Interference bands showed up (Fig. 17-11), indicating that the beam was diffracted as it passed through the slits. The crests and troughs from the two diffracted rays alternately added together and canceled out as they arrived at various points on the film. This would happen with a wave disturbance but not with stream of corpuscles—or at least not with any sort of particle ever imagined up to that time.

Fig. 17-11 . When photons pass through a pair of slits in a barrier, a wave-like interference pattern results.

However, it had been shown by other experiments that light has a particle nature. What about the pressure that visible light exerts? What about the discovery that its energy can be broken down into certain minimum packets? Is light both a wave and a particle? Or is it something else, something that is actually neither but with characteristics of both?

Suppose that photons are hurled one by one at a barrier with two slits and are allowed to land on a sensitive surface? Experiments of this sort have been done, and interference bands appear on the surface no matter how weak the beam. Even if the source is made so dim that only one particle hits the surface every minute, the pattern of light and dark bands appears after a period of time long enough to expose the film (Fig. 17-12). This pattern changes depending on the distance between the two slits, but it is the same pattern at all energy intensities.

Fig. 17-12 . How can “wave particles” pass one by one through a pair of slits and still produce an interference pattern?

What happens in experiments like this? Do photons “know” where to land on the film based on the wavelength of the light they represent? How can a single photon passing through one slit “ascertain” the separation between the slits, thus “knowing” where it “can” and “cannot” land on the film? Is it possible that a photons split in two and pass through both slits at the same time? Does some effect take place backwards in time so that the photons from the light source “know” about the sort of barrier they are going to have to pass through?

Researchers have a saying: “One theorist can keep a thousand experimentalists busy.” The double-slit experiments show that the converse of this is also true. In the quest for knowledge, turnabout is fair play.

Practice problems of these concepts can be found at: Wave Phenomena Practice Test

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