ELECTRIC CHARGE AND ELECTRIC FIELD
General Physics
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Dr. Brahmia 1
PARTICLES AND WAVES
• Blackbody Radiation
– At any temperature, any object
emits electromagnetic radiation
called thermal radiation.
– Thermal radiation consists of a
continuous spectrum,
encompassing wavelengths from
the visible, ultraviolet, and
infrared portions of the spectrum.
– From the classical point of view,
electromagnetic radiation is
generated by accelerating
particles. The distribution of
accelerations produces a
continuous spectrum.
PARTICLES AND WAVES…
• Planck’s Hypothesis
– In 1900, developed a theory that was in complete
agreement with the experimental evidence. Planck asserted that
the molecules in the heated object can vibrate only with discrete
amounts of energy. Thus, the energy of the vibrating atom is
quantized.
– where n, a whole number, is the quantum number, f is the
frequency of the resonator, and h is a constant, now known as
Planck’s constant, given by
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PARTICLES AND WAVES…
• The Photoelectric Effect
– When light is incident on certain
metals, electrons are ejected from
the surface of the metal almost
instantaneously. This is called the
photoelectric effect.
– The electrons are ejected from the
surface of the metal only if the
energy of the light is sufficiently
– Notice that photoelectrons, as they
are called, are drawn to the
positive collector, thus producing a
photocurrent.
FunctionWork W max0 KEWhf
PARTICLES AND WAVES…
• The Photoelectric Effect
– 1) The number of electrons emitted per
second (photocurrent) increases as the
intensity increases. The maximum kinetic
energy of the electrons is not affected by
the intensity of the light.
– 2) The maximum kinetic energy of the
photoelectrons is increased when the
energy of the photons is increased.
– 3) Below a certain frequency, called
threshold frequency, no electrons are
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PARTICLES AND WAVES…
• Problem 1
– Electrons are ejected from a metal surface with speeds ranging up
to 3.10×105 m/s when light with a wavelength of λ = 540 nm is
a) What is the work function of the surface?
b) What is the cutoff frequency for this surface?
PARTICLES AND WAVES…
• Pair Production
– A high energy photon known as the gamma ray traveling near the
nucleus of an atom may disappear and an electron and a positron
may appear in its place.
– The electron and the positron have the same mass and carry the
same magnitude of electric charge; however, while the electron is
negatively charged, the positron carries a positive charge.
– The charge, momentum, and mass-energy must all be conserved.
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• Pair Annihilation
– The opposite process of pair production is called pair annihilation.
In this case, instead of two antiparticles being produced, two
antiparticles next to each other (and essentially at rest) destroy each
other, producing two identical photons with opposite momentum (a
single photon cannot be created). The following diagram depicts
pair annihilation.
PARTICLES AND WAVES…
PARTICLES AND WAVES…
• Problem 2
– What is the minimum energy of a photon required to produce a
proton-antiproton pair?
– Note: the antiproton has the same mass as a proton but negatively
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• Wave-Particle Duality
– Louis de Broglie postulated:
– All particles exhibit both wave and particle characteristics.
– The wavelength (), momentum (p) and kinetic energy of a particle
with mass (m) are related by the following equations:
– where m and v are the mass and the velocity of the particle.
– In 1927, Davisson and Germer demonstrated that electrons can be
diffracted, just like electromagnetic waves.
PARTICLES AND WAVES…
• Wave-Particle Duality…
– Since photons do not have mass, the momentum (p) and the total
energy of a photon (E) are related by the following equation:
– where (c) is the speed of light, () is the photon wavelength and h is
the Planck’s constant.
PARTICLES AND WAVES…
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PARTICLES AND WAVES…
• The Uncertainty Principle
– was also responsible for a concept called the
uncertainty principle.
– The uncertainty principle states that it is fundamentally and
unquestionably impossible to make simultaneous measurements of
a particle’s position and velocity with arbitrarily large accuracy.
– An alternate form of the uncertainty principle applies to the
simultaneous measurement of energy and time.
• Problem 3
– A Nitrogen molecule travels at 515m/s. Suppose the uncertainty in
an experimental measurements of its speed is 5.0%. Compute the
minimum uncertainty in its position.
PARTICLES AND WAVES…
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PARTICLES AND WAVES…
– In 1923, shot a beam of X-rays at a block of
graphite. He found that the wavelength of the X-rays was longer,
and therefore the energy was smaller. Furthermore, he found that
the amount by which the energy was reduced was dependent on the
angle at which the X-rays were scattered.
PARTICLES AND WAVES…
• Compton scattering…
– Applying the laws of conservation of energy and momentum to the
collision, we can predict the wavelength change by the following
– where m0 is the rest mass of an electron, h is Planck’s constant, and
c the speed of light.
– The quantity (h/ m0 c) is called the Compton wavelength and is
approximately 0.00243 nm.
cos1
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PARTICLES AND WAVES…
• Problem 4
– An X-ray of wavelength 0.1000 nm is scattered by an electron. In
the resulting collision, the scattered photon is reflected directly
backward while the electron travels in the direction of the incident
photon. Determine the
– a) wavelength of the scattered photon and
– b) energy of the recoil electron.
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