Download Lecture 11 February 4, 2002 Chapter 3 The Particlelike Properties of

Lecture 11
February 4, 2002
Chapter 3
The Particlelike Properties of Electromagnetic Radiation
Sparks in Gases: Line Spectra
This is one of the oldest tools available for the investigation of atoms and radiation.
The experimental arrangement is to have two small metal plates inside a glass container
from which the air was gradually removed by a pump (not included in the figure). The
plate connected to the negative side of the electricity supply is called the cathode and that
to the positive side is called the anode. As the pressure was lowered, a spark appeared
going from the cathode to the anode. What do you expect when the air pressure is
reduced further and further? We now know that what happened here is field emission of
electrons when a strong electrostatic field is applied, e.g. using a high voltage or making
a tip as sharp as you can, which will lower the potential barrier between the solid and the
vacuum. If the barrier is low enough electrons can tunnel through the barrier. This, of
course, is not known in the 19th century. The emitted energetic electrons will then collide
with atoms in the tube and excite the atoms into high energy levels causing subsequent
emission of electromagnetic radiation.
When the tube is filled with a certain gas, such as H2 or He, sustained glow with
characteristic color can be achieved. Detailed analysis shows that the line spectra from
such glow consist of lines with well-defined discrete wavelengths. For example, the
spectrum of hydrogen exhibits four visible lines and many ultraviolet lines as observed
early on. Johann Balmer succeeded in obtaining a simple empirical formula given by
k2
λ = 364.56 2
nm
k − 4
where k is an integer and k>2. The explanation of this empirical formula is one of the
great successes of the Bohr model of hydrogen.
How do you measure the wavelength of the radiation? You will learn how to do
this in the lab.
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Cathode Rays
When the pressure in the discharge tube is reduced to a very good vacuum, do you
expect anything to happy? Yes, things still glow, although differently! The glow is not
in the middle of the tube but on the glass wall of the tube. It was found that a ray was
emitted by the cathode, called the cathode ray. We now know that the cathode ray
consists of electrons. The effort to understand the nature of the cathode ray led to many
great discoveries.
Hertz and Lenard, discovered in 1891 that the rays could penetrate a thin
aluminum plate, and can be detected in the air just outside the tube (very close to the Al
film). In 1897, J. J. Thomson showed that the cathode ray consists of negatively charged
particles, and he measured e/m, the ratio of charge to mass for a single particle. He
achieved this with a specially designed cathode ray tube, the precursor of the tube in a
present-day TV set.
The cathode was at the far narrow end of the tube, the anode a few centimeters away,
with a small hole in its center. The rays went from the cathode to the anode, but a narrow
beam continued through the hole in the anode to the glass at the other end of the tube,
where their impact caused the glass to glow in a small central spot. Inside the tube two
parallel plates are placed so that the narrow beam of cathode rays went between them on
its way to the end of the tube. Thomson found that electrically charging these plates
caused the beam to deflect, so the glowing spot moved from the center of the end of the
tube. Thomson also added magnets to give a uniform magnetic field in the region
between the plates. By adjusting this magnetic field strength to cancel the deflection of
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the rays caused by the electric field, he was able to measure the speed of the rays,
because of the balancing these two forces
eE = ev x B .
From here the speed, which is the ratio of electric field strength to magnetic field
strength, is determined.
Having determined the horizontal speed vx the charge to mass ratio can be
determined by measuring the deflection in the electric field alone. In this situation, the
downward force is eE, and it operates for a time L/vx, where L is the length of the plates.
Inside the plates the particle acquires a vertical speed of (v=at)
eE L
vy =
.
m vx
On emerging from the region between the plates, the electron moves in a straight line,
now at an angle θ given by
tan θ =
vy
vx
=
eE L eE
L
e LB 2
=
=
m v x2
m ( E / B) 2 m E
The value of e/m that emerged from this experiment was a complete surprise. It was
about 2,000 times the value for the hydrogen ion, which has the largest value of any ion.
Once it had been established that the cathode rays were not just uncharged
electromagnetic waves, it had been assumed that they were "molecular torrents" - a flood
of the same kinds of ions found in electrolysis. Now, apparently, the cathode rays were
particles smaller than the smallest atom! This was the first hint that atoms might be made
up of smaller entities. Another important point is that Thomson found this ratio e/m to be
independent of the material the cathode was made of. The cathode rays could have been
fragments of atoms which were different for different atoms, but evidently this was not
the case. Furthermore, he found in 1899 that photoelectrically produced particles had the
same e/m, so were probably the same particles.
Is this the end of the story? No!
X-rays
In 1895 Wilhelm Roentgen was checking out the work of Hertz and Lenard on
cathode rays, and in particular was interested in Lenard's discovery that the rays
penetrated a little way into the air if the tube had an aluminum window. He had covered
his tube with black cardboard and darkened the room to check that no light was getting
through, and suddenly he noticed a weak light shimmering on a little bench nearby. The
source of the mysterious light was a fluorescent screen for detecting ultraviolet light. But
if the tube was producing any ultraviolet light, it wouldn't make it through the cardboard,
and the cathode rays themselves only traveled a few centimeters in air. The little screen
was a meter away from the tube. Roentgen concluded that the tube must be emitting
some new radiation of an unknown type, he called "x-rays".
He found that the x-rays traveled in straight lines, and (unlike the cathode rays)
were not deflected by magnetic fields. He found they passed through flesh almost
unimpeded, but bone cast a shadow. By having his wife place her hand between the point
source of x-rays on the Crookes' tube and some unexposed film in a box, then developing
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the film, he took a picture of the bones in her hand. On January 1, 1896 he announced his
findings, complete with the bone picture, to many of his colleagues, and remarked to his
wife "Now the fun begins".
X-ray production
The physical picture of x-ray production is that the emitted and accelerated
electrons suddenly decelerate on hitting the target, unloading their kinetic energy as
radiation (plus some heating of the target). This deceleration radiation is called
bremsstrahlung (braking radiation). The schematic below shows the apparatus for x-ray
production in which electron emission is assisted by thermal excitation (thermionic
emission).
In general electrons undergo many collisions in the process of deceleration inside the
target and produce many photons and phonons (heat). Photon with the largest energy is
created when the electron undergoes just one collision and gives up nearly all its energy
to the photon. In this case,
hc
eV0 = hν max =
λmin
where V0 is the accelerating voltage. Thus,
hc 1 1240eV •nm
λmin =
=
.
e V0
eV0
For V0=35keV, λmin = 0.0354nm = 0.354Å . This minimum wavelength is independent
of the target used. However, the intensity of the x-ray depends on the ability of the
electric field of the target’s atoms in decelerating the electrons. Thus, targets with
heavier atoms are more efficient in producing x-rays. The intensity is proportional to the
square of the atomic number Z of the target atoms. The intensity is also proportional to
the square of the voltage used to accelerate the electrons. The figure below shows data
with V0=35keV. The discrete lines are explained later in Chapter 8, Moseley’s law.
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