Transcript Slide 1

PARTICLE-LIKE PROPERTIES OF LIGHT
(or, of electromagnetic radiation, in general) – continued
Let’s summarize what we have said so far:
I.Arguments supporting the wave-like nature of light:
● Young’s double-slit experiment;
● Diffraction phenomena (Newton tried to explain diffraction
effects using his theory, but his explanations worked only
for very simple situations, e.g., “pinhole diffraction”, but not
for pronounced effects, such as those seen in experiments
with diffraction gratings).
● Maxwell Equations and the results of many experiments
that confirm their validity.
II. Arguments supporting the particle-like nature of light:
● Photoelectric effect.
So far, in this list there is only a single argument in favor of
particle-like nature.
But the list is not finished yet! More arguments can be added to
Part I, as well as to Part II of the above list.
Let’s continue the story…
Pronounced wave-like properties (interference, diffraction) can be
Observed for “soft forms” of electromagnetic radiation (such as
“radiofrequency radiation” used in wireless communication, or the
waves used in radars – they are called “microwaves” and they are
also used in microwave ovens).
On the other hand, “soft” electromagnetic radiation does not cause
any photoelectric effect – it occurs only for “harder” radiation, i.e.,
visible light, or even harder than visible light, such as ultraviolet
radiation.
So, perhaps “softer” EM radiation has a wave-like nature, and with
“hardening” it changes to a particle-like nature?
This is only partially true: indeed, when the frequency increases (i.e.,
the wavelength becomes shorter), the particle-like properties are
More strongly manifested – but the wave-like properties DON’T GO
AWAY, OH, NO!
Example: scattering of X-rays by crystals. It is evidently diffraction!
About X-rays
In 1895, Wilhelm Konrad Röntgen, a German
physicist, discovered an entirely new form
of radiation. He found that this radiation had
many amazing properties. But because its
nature was a total mystery for him, he called
it “X-rays”.
For more than 10 years the “mystery”of X-rays
remained unsolved – nonetheless, Röntgen
was awarded the first-ever Nobel Prize (1901),
and people started using the new “see-throught”
radiation in medical diagnostics and formany
other practical purposes. That X-rays offer
fantastic new opportunities beacame
Clear just weeks after the moment of
Discovery: here are examples of early
X-rays made in Röntgen’s lab. In one of
them you can see the image of bones in
the palm of Mrs. Röntgen’s hand.
Quick quiz: can you tell, was she an American,
or rather you would say she was from Europe?
The nature of X-rays remained a “mystery” until…
...another German scientist, Max von Laue, and two British scientists,
Bragg father and Bragg son, started shining X-rays on crystals.
It turned out that crystals act as 3-dimensional diffraction gratings
for X-rays!
JAVA Laue : using this link, you can simulate X-ray diffraction images.
Examples of X-ray diffraction images (so-called “Lauegrams”):
Spahalerite (a mineral)
From a “quasicrystal” – do you
see that something is unusual?
After von Laue’s and Braggs’ experiments, it became
clear that X-rays simply belong to the family of
electromagnetic waves.
The diffraction effects are strongly manifested in crystals, because the
typical wavelengths of X-rays (0.1-10 nm) are comparable to the
interatomic spacing of crystals.
QUESTION: Why we don’t observe diffraction of visible light in crystals?
How does diffraction work in crystals? We will try to explain that
using math and some helpful pieces of graphic.
X-ray scattering by a single atom:
Impinging
plane wave
Scattered
spherical
wave
von Laue’s approach to X-ray diffraction by crystals:
Let’s begin with the smallest possible “crystal” one can conceive:
namely, one consisting of just two atoms:
Important question: what is the phase shift when a wave is reflected from
a hard object? (shift between the incident and the reflected or scattered
wave)?
The Braggs used a different approach:
They considered reflection from
the planes of atoms in a crystal.
Braggs’ approach and results are
now widely used, because their
Way of handling the problem leads
To a particularly simple equation
Expressing the conditions at which
A reflection may occur: it’s called
“the Bragg Law”, “the Bragg condtion”, or simply “the Bragg
equation”.
The Bragg Equation:
Here it is shown how the Bragg Eq. is
derived: the difference in the “optical
paths” of the waves reflected from two
adjacent atomic planes must be a whole
number of λ-s in order to result in
constructive interference.
The rest is just highschool trigonometry….
n  2d sin  ; n  1,2,3,
Practical example:
NaCl crystal (table salt): d = 5.65 nm
X-rays:  = 0.154 nm (commonly used wavelength from a “copper” tube.
Task: find the diffraction angle of the first reflection, if you rotate the
Crystal, starting from θ = 0.