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CLASS 29. THE NUCLEUS IS MADE OF PROTONS AND NEUTRONS
29.1. INTRODUCTION
Nuclear physics is the subfield of physics that studies the building blocks of the nucleus and how
those building blocks are put together. Rutherford’s model of the atom being made up of a densely
packed, positively charged nucleus and electrons, with most of the atom being empty space
explained most of the data observed. The next question was whether the nucleus was made up of
other, more fundamental pieces.
29.2. GOALS
• Explain what isotopes are and how they can be identified;
• Understand what mass number represents;
• Explain how artificial transmutation occurs and how it differs from radioactive transmutation;
• Understand how cloud chambers work and how they assisted study of the nucleus;
• How the neutron was discovered;
• How the proton-electron model of the nucleus evolved into the proton-neutron model of the
nucleus; and
• Be able to read and use shorthand notation for isotopes.
29.3. ISOTOPES
In 1911, Thomson applied the same techniques he
had used to discover the electron to study the newly
Beam of ions
discovered nucleus. He focused beams of neon ions
q
through a magnetic field. Recall that the curvature of
the path these particles take in a magnetic field B is
R1
given by:
R=
mv
qB
R2
where m is the mass of the particle, q is the charge of
the particle and v is the speed of the particle.
If all neon ions are identical and they are traveling at
the same speed, they should follow the same path. Figure 29.1: Ions from different isotopes of
To Thomson’s surprise, they didn’t – they followed the same element follow different paths in a
two distinct paths. He knew from measurements in magnetic field.
an electric field that all of the neon ions had the same
charge. The only possibility was that different atoms of neon had slightly different masses.
The atomic mass of neon is 20.179 u; Thomson showed in 1912 that neon atoms come in two
different masses (there are three masses, but Thomson found only two of them). Thomson found
neon with atomic mass = 20 u and atomic mass = 22 u. Later scientists found neon atoms with
atomic mass = 21 u. We call these different ‘versions’ of an element that have different masses
isotopes.
29.3.1. Mass Number and Shorthand. To differentiate between atoms of the same element with
different masses, isotopes are referred to by their name and mass. The isotope of neon with mass 20
u is Ne-20. The mass number of an element, which is represented by A, is an integer that reflects the
particular isotope of an atom. The mass number of Ne-20 is 20. The mass number of Ne-22 is 22.
We can specify an isotope using a shorthand notation. An atom with atomic number Z and mass
number A has Z protons and Z electrons. We would represent Ne-20 (which has a mass number of
20 and an atomic number of 10) as 1020 Ne . The top left-hand number represents the mass number and
the bottom left-hand number is the atomic number. Using this shorthand provides you with
important information about the particular isotope.
29.4. ARTIFICIAL TRANSMUTATION
29.4.1. The Data. In 1919, Rutherford discovered that hitting an element with very energetic α
particles could change the target element into another element. When Rutherford hit nitrogen gas
molecules with alpha particles, he found evidence of hydrogen. Rutherford thought that the
hydrogen might be coming from the radium source (from the alpha particles came), but he found
experimentally that the hydrogen was coming from the nitrogen gas. Further measurements showed
that some of the nitrogen atoms were changing into oxygen atoms when they were hit by the alpha
particles, with hydrogen also being formed.
29.4.2. The Mechanism. The most important implication of this experiment was that nitrogen
somehow contained hydrogen and that hydrogen could be freed when the nitrogen was bombarded
by energetic alpha particles. The next question was how this happened.
Hydrogen is the lightest of all elements (Z = 1). In 1815, Proust proposed that (even though a very
small number of atomic masses were known) that all atomic masses are multiples of the atomic mass
of hydrogen. When elements like chlorine (which had a mass of 35.46 u that clearly was not a
multiple of the atomic mass of hydrogen) were discovered, the theory was discarded. Thomson’s
discovery of isotopes was cause to reconsider Proust’s theory.
According to the Rutherford model of the atom, the hydrogen atom had one electron and the
hydrogen nucleus had charge +e. The positive charge of any nucleus could be accounted for by an
integral number of hydrogen nuclei charges. This suggested to Rutherford that the hydrogen nucleus
was a fundamental entity – perhaps the building block scientists had been looking for. Rutherford
named the hydrogen nucleus the proton, from the Greek word protos meaning "first."
The process of changing one atom into another by hitting it with an energetic particle is called
artificial transmutation, in contrast to the radioactive elements, which transmuted into other
elements without any external nudging. Although the first artificial transmutation was accidental, it
showed scientists that other transmutations might be possible if the right ‘bullet’ could be used. The
α particle had limited potential: alpha particles were obtained from naturally radioactive materials
and their speed could not be controlled. This, combined with the small mass of the alpha particle,
prohibited inducing artificial transmutation of heavier elements.
29.5. THE PROTON-ELECTRON MODEL
Remember that Rutherford’s model of the atom was
troubled because the electrical charge of the nucleus
and the electrons should cause the electrons to be
attracted to the nucleus. Rutherford suggested that
nuclei must be built of protons and electrons that
were bound together by electrostatic forces. There
would have to be the same number of protons and
electrons because an atom is electrically neutral.
The proton-electron model has a nucleus that
contains A protons and A-Z electrons, with Z
additional electrons outside the nucleus, where A is
the mass number . In this model, fluorine would
have 18 protons and 9 electrons in the nucleus, and Figure 29.2: The proton-electron model of
9 additional electrons outside the nucleus, as shown the atom. The protons are blue and the
electrons are yellow
in Figure 27.3.
Why did Rutherford place the electrons inside the nucleus? He knew that alpha particles are emitted
from atoms. The α particle has a mass of 4 u and a charge of +2e. If each proton has charge +e, you
need four protons to get the right mass, and two electrons to account for the charge. If the alpha
particle is emitted from the nucleus, Rutherford reasoned that the electrons should be in the nucleus
with the protons.
29.6. DISCOVERY OF THE NEUTRON
29.6.1. Predicting the Neutron. In 1920, Rutherford suggested that a proton inside the nucleus
might have an electron so closely bound to it that it essentially formed a neutral particle, which he
called a neutron. Finding a neutron is harder than finding a proton or electron because a neutron – if
it existed – would not have any charge and thus could not be manipulated electric and magnetic
fields.
The discovery of artificial transmutation suggested that one approach would be was to either engage
a neutron in a collision, or induce a collision that produced a neutron. Many experiments were tried.
J. L. Glasson, a student at the Cavendish Laboratory, tried to aim high-velocity protons toward a
cathode-ray beam with the hope that some protons might combine with electrons to form neutrons.
If any of the neutrons entered a heavy nucleus, the collision would disrupt either the nucleus or the
neutron, thus producing charged particles that could be detected. This experiment was unsuccessful
in observing any neutrons.
In 1930, W.G. Bothe and H. Becker found that when boron (B) or beryllium (Be) were bombarded
with α particles, they emitted a type of radiation that had no electric charge. The new radiation
could penetrate 200 millimeters of lead. (It takes less than one millimeter of lead to stop a proton.)
They deduced that the neutral radiation must be high-energy gamma rays.
Marie Curie's daughter, Irene Joliot-Curie, and Irene's husband, Frederic Joliot, put a block of
paraffin wax (which has a lot of hydrogen in it) in front of the radiation emitted from beryllium
bombarded by α particles. They observed high-speed protons coming from the paraffin. They knew
that gamma rays could eject electrons from metals and thought that the same thing was happening to
the protons in the paraffin; however, analyzing their reactions showed that there was no way that
gamma rays – even very high energy ones – could be responsible for ejecting the protons. The
radiation must be something other than gamma rays.
Chadwick, who had been working with Rutherford, left for Berlin in 1913 to work with Hans
Geiger. World War I broke out the following year and the British Chadwick was detained as a
civilian prisoner of war. Despite being allowed to read books and talk to other physicists, he could
not do experiments. In 1918, the war ended and Chadwick returned to Manchester to work on
transmutation. When Rutherford went to Cambridge in 1919 to become director of the Cavendish
Laboratory, Chadwick went with him to continue his search for the neutron. He tried experiments in
1923 and 1928 without success.
The experiments of Curie and Joliot (and others) suggested to him that the new radiation must be
due to particles with a mass close to the mass of the proton. He posited that this new radiation was
actually the long-sought-after neutron. Chadwick suggested that, when an element such as beryllium
is bombarded with α particles, the reaction that takes place is:
4
2
He + 49 N → 126 O + 01n
where 01n is the neutron (no charge, 1 atomic mass unit).
Chadwick generated the mysterious beryllium rays – which he thought might be neutrons – and put a
target in the path of those rays. When the beryllium rays hit the target, they knocked charged atoms
out of it. The charged atoms were detected. He used a number of different targets and analyzed the
results using the ideas of conservation of momentum and conservation of energy. The only good
explanation for all of the data he collected was a neutral particle with a mass close to the mass of the
proton. Chadwick determined the mass of the neutron to be 1.16 u. The accepted value of the
neutron mass today is 1.008665u.
29.7. THE PROTON- NEUTRON MODEL OF THE ATOM
29.7.1. The Theory. This leaves us at a theory in which an atom with atomic number Z and mass
number A has Z protons and A-Z neutrons comprising the nucleus. 1020 Ne tells you that there are 10
protons (Z = 10) and 20 neutrons + protons (A + Z = 20). In other words, the notation is
# neutrons + # protons
# protons
E
where E is the symbol for the element. The particles in the nucleus, whether neutrons or protons,
collectively are called nucleons. Z electrons were outside the nucleus, although the question of why
they weren’t attracted to the nucleus remained open. This is the model you probably learned in high
school.
29.7.2. Implications of the Proton-Neutron Model
• The model of the neutron changed from Rutherford’s original idea of a combination
electron/proton to the neutron being a fundamental particle, just like the proton and electron.
• The α particle changed from being four protons and two electrons to being two protons and two
neutrons. This is consistent with the emission of alpha particles from the nucleus.
• This model explained alpha decay due to the experiments in the cloud chamber; however, β
decay became more difficult to explain. If electrons weren’t in the nucleus, removing an
electron should be just like ionizing the element. There must be something more to β decay.
29.8. BETA DECAY
The explanation for beta decay didn’t come until much later. In 1930, Wolfgang Paul proposed the
existence of a hitherto unobserved neutral and massless particle, in order to explain beta decay.
Enrico Fermi used this particle, which he called a neutrino (little neutron) in his theory of radioactive
decay. The neutrino was not observed experimentally unitl 1959. The neutrino is represented by a
Greek letter ν.
Beta decay is thus the result of the decay of a neutron into a proton, an electron and a neutrino.
1
0
n → 11 p + −10 e + ν
Since the neutrino has neither charge nor mass, it doesn’t have any numbers associated with its
symbol.
29.9. EXPLAINING ARTIFICIAL TRANSMUTATION
29.9.1. The Experiment. Rutherford and co-worker James Chadwick (1891-1974) aimed α
particles at other elements and found similar transmutation effects. All the light elements from B to
K could be induced to expel a proton when hit with an alpha particle. Rutherford and Chadwick
couldn’t detect an expelled proton in carbon and oxygen, but later researchers were able to observe
it. There are two possible explanations for this phenomenon.
The first possibility is that the nucleus of the bombarded atom loses a proton as a result of a collision
with the α particle. This is called alpha scattering because the alpha particle comes out after the
scattering. We can express the transmutation using the shorthand notation introduced above.
4
2
He + 147 N → 136 C + 24 He + 11H
a
The above equation says that an alpha particle ( 24 He ) plus nitrogen yields C-13, the alpha particle
and a proton.
The second possibility is that the α particle is captured by the nucleus of the atom, which forms a
new nucleus plus a proton. This is called alpha capture because the alpha particle is incorporated
into the nucleus.
4
2
He + 147 N → 178 O + 11H
b
The left-hand side of the second equation is the same as the first equation; however, the results of the
collision are different. The two equations are represented graphically in Figure 29.3.
proton out
α in
proton out
α in
Nucleus moves
slightly after hit
Nucleus moves
slightly after hit
α out
Figure 29.3: Case I: A proton is knocked out Case II: The alpha particle is absorbed by the
and the alpha particle is scattered
nucleus and the proton is knocked out.
The primary difference between the two cases is the following: in the first case, the nucleus would
be lighter after the α particle was ejected. In the second case, the nucleus would be heavier after the
collision. The key would be to be able to determine what was coming out after the collision.
29.9.2. The Cloud Chamber: A New Way of Detecting Particles. The earliest techniques for
detecting particles were basically watching for flashes of light on a scintillating screen. This was
tedious, not always precise, and prone to human error. The cloud chamber was invented by C.T.R.
Wilson (1869-1959). A cylinder filled with gas is rapidly cooled so that it is supersaturated (heavily
loaded) with water vapor. A particle entering the chamber ionizes the gas in its path. Water vapor
condenses on the ions created along the path, making a track that can be seen. This is the same
mechanism responsible for forming contrails from jet airplanes. Wilson and Arthur Compton won
the Nobel Prize in 1927.
The advantage of the cloud chamber is
that multiple particles can be observed, all
at the same time. Magnetic or electric
fields can be applied and the path of the
tracks helps to identify what type of
particle made the track and what types of
6
interactions the particle might have Figure 29.4 A cloud chamber, showing β particles
(electrons) in a magnetic field.
undergone.
Figure 29.4 shows the tracks of electrons in a cloud chamber. A magnetic field is applied –
otherwise, the particle tracks would be straight. The βs enter from the upper left corner. The β
particles must be traveling at different speeds because they are following different paths.
6
http://www.sciencemuseum.org.uk/on-line/electron/section3/1937.asp
29.9.3. Using the Cloud Chamber to Resolve Artificial Transmutation. The cloud chamber
allowed scientists to differentiate between the two
Case a
possibilities described by Rutherford to explain artificial
transmutation. For the first case (the alpha particle is
scattered from the nucleus), there should be a track for the
incoming α, a track for the α after collision, a track for the
proton out
proton coming out, and the recoil from the atom after the
α in
collision. If the second case (the alpha is captured by the
Nucleus moves
nucleus) was correct, there would not be a track from the
slightly after hit
outgoing α because it would have been captured by the
nucleus.
α out
In 1925, P.M.S. Blackett repeated Rutherford’s experiment
of alpha particles hitting nitrogen gas, but he performed the
Case b
experiment using a cloud chamber. Figure 29.5 shows the
possible tracks you might expect for the two possibilities
described above. His results confirmed that the second
proton out
theory is correct. The α particle is captured by the nucleus
α in
of the atom it hits, which forms a new nucleus that emits a
Nucleus moves
proton.
slightly after hit
4
2
He + 147 N → 178 O + 11H
29.10. APPLICATIONS OF ISOTOPES
Element
Atomic mass
Carbon
14
14
β
Used in carbon dating.
32
32
P
β
Useful as biological tracer
40
40
K
β, γ
Naturally occurring in our bodies
Co
β, γ
Used in cancer treatment
Phosphorus
Potassium
Symbol
Figure 29.5: Two possibilities for
cloud chamber tracks
C
60
60
Strontium
90
90
Iodine
131
Cobalt
Type of radiation
Sr
β
β, γ
Used as a medical tracer
Rn
α, γ
A radioactive gas, produced by the decay
of Radium
α, γ
Used in medical treatment, and in old
luminous watch dials
Natural radioactive substance
Radon
220
Radium
224
224
Uranium
238
238
α, β
235
235
U
α
239
239
Pu
α, β
Plutonium
Produced by nuclear explosions
I
131
220
Uranium
Notes
Ra
U
Fuel for nuclear power stations
Man-made. Used in nuclear weapons
Table 29.1: Some common radioactive isotopes.
29.11. SUMMARIZE
29.11.1. Definitions: Define the following in your own words. Write the symbol used to represent
the quantity where appropriate.
1. proton
2.
isotope
3.
atomic mass number
4.
decay chain
5.
nucleons
6.
neutron
7.
neutrino
8.
alpha capture
9.
alpha scattering
29.11.2. Equations: No equations this chapter
29.11.3. Concepts: Answer the following briefly in your own words.
1. What is the difference between the proton-electron and the proton-neutron models of the atom?
2.
Explain in your own words how Thomson discovered isotopes. What was the particular
experimental result that led him to conclude that not all atoms of an element have the same
mass?
3.
What does Cl-37 mean? How would you represent Cl-37 in the shorthand introduced in this
section?
4.
When we left the last chapter, the alpha particle was four protons and two electrons. What was
the alpha particle posited to be after the discovery of the neutron?
5.
How many neutrons, protons and electrons are in the following?
6.
What elements are represented in the following (i.e. what is ‘X’)?
7.
What is the difference between radioactive transmutation and artificial transmutation?
8.
Why was the neutron difficult to discover?
9.
How is the proton-neutron model of the atom different than the proton-electron model of the
atom?
6
3
Li, 136 C , 1531P
31
15
X,
57
26
X , 109
47 X
10. Why did the alpha particles limit possible artificial transmutations in heavy elements?
11. Can you make elements heavier through transmutation? Why or why not?
12. Can you make elements heavier through artificial transmutation? Why or why not?
13. Can you make elements lighter through transmutation? Why or why not?
14. Can you make elements lighter through artificial transmutation? Why or why not?
15. What is the accepted mass of the neutron today?
16. Can all elements undergo radioactive transmutation? Why or why not?
17. Can all elements undergo artificial transmutation? Why or why not?
18. Can an atom that can radioactively transmute also undergo artificial transmutation? Why or
why not?
29.11.4. Your Understanding
1. What are the three most important points in this chapter?
2.
Write three questions you have about the material in this chapter.
29.11.5. Questions to Think About
1. What were the arguments that supported the idea that the hydrogen nucleus was a fundamental
building block of other atoms? Had this idea been considered earlier? If so, why was it not
pursued further?
PHYS 261 Spring 2007
HW 30
HW Covers Class 29 and is due March 26th, 2007
1.
a. How many neutrons, protons and electrons are in the following?
b. What elements are represented in the following (i.e. what is ‘X’)?
2.
3.
6
3
Li, 136 C , 1531P
31
15
X,
57
26
X , 109
47 X
What is the difference between radioactive transmutation and artificial transmutation?
How is the proton-neutron model of the atom different than the proton-electron model of the
atom?
29.12. RESOURCES
“A neutron walked into a bar and asked ‘how much for a drink’. The bartender looked at him and
said, ‘For you, no charge’.