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Chapter 3: Q9CQ (page 92)

A low-intensity beam of light is sent toward a narrow single slit. On the far side, individual flashes are seen sporadically at detectors over a broad area that is orders of magnitude wider than the slit width. What aspects of the experiment suggest a wave nature for light, and what aspects suggest a particle nature?

Short Answer

Expert verified

The particle nature of light shows flashes on the detector screen, while the diffraction of light proves the wave behavior.

Step by step solution

01

Concept used  

A low-intensity beam of light is sent toward a narrow single slit. On the far side, individual flashes are seen sporadically at detectors over a broad area that has an order of magnitude wider than the slit width.

02

Wave nature 

When light is sent from a single slit, it bends from the corner of slits. It forms a constructive and destructive pattern of interference. Forming interference pattern is the property of a wave. So, we can say light also exhibits wave nature.

03

Particle nature

When a very low-intensity of light beam passes through a single slit, the bright strips of light called flashes are recorded on the detector screen. That would only be possible if the beam having a bunch of particles strikes the detector's screen. This proves the particle behavior of light.

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Most popular questions from this chapter

A photon and an object of mass m have the same momentum p.

  1. Assuming that the massive object is moving slowly, so that non-relativistic formulas are valid, find in terms of m , p and c the ratio of the massive object鈥檚 kinetic energy, and argue that it is small.
  2. Find the ratio found in part (a), but using relativistically correct fomulas for the massive object. (Note: E2=p2c2+m2c4may be helpful.)
  3. Show that the low-speed limit of the ratio of part (b) agrees with part (a) and that the high-speed limit is 1.
  4. Show that at very high speed, the kinetic energy of a massive object approaches .

The electromagnetic intensity of all wavelengths thermally radiated by a body of temperature T is given by

I=蟽T4where蟽=5.66脳10-8W路m2路K4

This is the Stefan-Boltzmann Law. To derive it. show that the total energy of the radiation in a volume V attemperature T is U=8蟺5kB4VT4/15h3c3 by integrating Planck's spectral energy density over all frequencies. Note that

鈭�0鈭�x3ex-1dx=蟺415

Intensity, or power per unit area, is then the product of energy per unit volume and distance per unit time. But because the intensity is a flow in a given direction away from the blackbody, c is not the correct speed. For radiation moving uniformly in all directions, the average component of velocity in a given direction is14c .

An electron moving to the left at 0.8c collides with an incoming photon moving to the right . After the collision, the electron is moving to the right at 0.6c and an outgoing photon moves to the left. What was the wavelength of the incoming photon?

Compton used X-rays of 0.071nm wavelength. Some of the carbon鈥檚 electrons are too tightly bound to be stripped away by these X-rays, which accordingly interact essentially with the atom as a whole. In effect mein equation (3-8) is replaced by carbon鈥檚 atomic mass. Show that this explains why some X-rays of the incident wavelength were scattered at all angles.

From equations (3-4) to (3-6) obtain equations (3.8). It is easiest to start by eliminating 蠁 between equations (3-4) and (3-5) using cos2蠁+蝉颈苍2蠁 = 1 The electron speed u may then be eliminated between the remaining equations.
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