7 Electrons and nuclei copy a level physics edexcel
1. 7.1
The language of
the atom
p. 113-114
Define the following terms about the atom of an element :
• atomic number,
• mass number,
• neutron number,
Atomic number, , or proton number is the number of protons
in the nucleus of an atom.
Mass number, , or nucleon number is the number of
nucleons (protons and neutrons) in the nucleus of an atom.
Neutron number , , is the number of neutrons in the nucleus
of an atom.
𝑋
𝑍
𝐴
2. 7.1
The language of
the atom
p. 113-114
1. What is the relationship between , , and ?
2. How does the number of electrons relate to the number of protons in an atom?
Explain the consequence this has on the charge of the atom.
3. Define the term “isotope”.
𝑋
𝑍
𝐴
Isotopes are atoms of the same element with different neutron numbers .
3. Copy and complete the table below.
7.1
The language of
the atom
p. 113-114
lead Pb 82 207 82 125 82 lead-207
Pb 82 122 82 lead-204
13 27 13 14 13 aluminium-27
gold Au 79 118 79
beryllium Be 9 4 4 beryllium-9
5. 7.2
Alpha particle
scattering
p. 114-117
1. What two significant observations were made by Rutherford’s team?
2. To what conclusions might these observations have led to?
Observation 1: Most of the alpha particles passed straight through.
Conclusion 1: Most of the atom is empty space and most of its mass is concentrated in a small region, the
nucleus.
Observation 2: Some alpha particles were deflected through angles of more than 90.
Conclusion 2: Most of the charge of the atom is concentrated in the nucleus.
7. 7.2
Alpha particle
scattering
p. 114-117
Assume an alpha particle with kinetic energy rebounds back with a scattering
angle of 180° when deflected by a gold () nucleus.
If the scattering can be modelled from Coulomb’s law, calculate the closest
distance the alpha particle and the gold nucleus can get (consider that all the
kinetic energy is transferred to electrical potential energy).
Extension: The calculation above gives an upper limit for the radius of the gold nucleus. Explain how the
calculation would be affected if more energetic alpha particles were used and then comment on the
precision of the method to determine the radius of a nucleus.
𝐸𝑘=𝑉𝑄 ∴1.2 ×10
− 12
=
𝑘𝑞
𝑟
𝑄∴ 𝑟=
𝑘 ×2 𝑒×79 𝑒
1.2 ×10
− 12
=3 ×10
−14
𝑚
8. 7.2
Alpha particle
scattering
p. 114-117
The order of magnitude value for the radius of atoms is while the order of
magnitude value for the radius of nuclei is .
In a visual model of the atom, the nucleus is represented by an apple of diameter 8 cm. Estimate the
diameter of the atom in this model.
Extension: A tiny droplet of oil diameter 1.0 mm is placed on water. The oil spreads out as a circular disc of
thickness approximately one atom thick. Estimate the radius of this oil disc.
9. 7.3
Thermionic
emission
p. 117
When a piece of metal is heated to a high temperature, electrons ‘bubble’ out of
its surface. This is called thermionic emission.
In electron guns, a positively charged plate is placed near such a piece of metal
in a vacuum, accelerating the electrons towards it in the form of a narrow beam.
Describe and explain the direction of the magnetic field
that curves the path of the electrons emitted by the
electron gun in the image.
10. 7.4
Some useful
algebra
p. 118
Show that the radius of curvature of the electron beam can be given by the
equation and subsequently the frequency at which the electrons circle is given by
the equation .
11. 7.4
Some useful
algebra
p. 118
A mass-spectrometer is an instrument that is used to measure the masses of
molecules. Molecules of a gas are ionised and travel through a vacuum in a narrow
tube. The ions enter a region of uniform magnetic flux density B where they are
deflected in a semi-circular path as shown.
(a) State why it is necessary for the molecules to
be ionised.
(1)
(b) State the direction of the magnetic field.
(1)
(c) The ions have a charge of +e and a speed of
1.20 × 105
m s−1
. When B has a value of 0.673 T,
the ions are detected at a point where the
diameter of the arc is 14.8 cm. Calculate the
mass of an ion.
(3)
(d) Ions with a smaller mass but the same charge
and speed are also present in the beam. Sketch
the path of these ions in comparison with the
path of the heavier ones.
(1)
13. 7.5
The cyclotron
p. 119-120
A cyclotron is a particle accelerator with two semi-circular flat metal boxes (Dees)
open at their diameter at the centre of which a source of protons is placed. The
Dees are connected to a high-frequency alternating voltage, and situated in a
strong vertical magnetic field, with the whole set-up in vacuum.
• Protons that emerge from the central source enter one of
the Dees and follow a semi-circular path due to the action
of the magnetic field.
• When they return to the gap, a negative p.d. accelerates
them across it.
• The protons enter the second Dee with more kinetic
energy, so the semi-circle has a greater curvature.
• The frequency of alteration of the voltage supply is double
that of the frequency of circulation of the protons, so the
protons will again face an accelerating negative p.d.
• Kinetic energy is added each time, so the protons keep
spiralling outwards until they leave one of the Dees
tangentially.
14. 7.5
The cyclotron
p. 119-120
* The diagram shows the basic structure of a cyclotron.
With reference to the magnetic field and the alternating potential difference
explain how the cyclotron produces a beam of high speed particles.
(4)
16. 7.6
Linear
accelerators
p. 120-121
A linear accelerator (linac) is a particle accelerator in which charged particles
pass between charged metal tubes with energy delivered to them in every small
gap between the tubes.
• A high-frequency alternating voltage supply ensures the accelerating particles always face the opposite
charge from one tube to the next.
• The length of the tubes increases as the speed of the particles increases to ensure they spend the same
amount of time in each tube.
• The particles drift (travel at steady speed) within each tube.
17. 7.7
Particle
detectors
p. 122-123
Energetic charged particles cause ionisation in any material through which they
pass allowing for their detection in particle detectors.
Particle detector What is ionised? How is the path of the particle detected?
Cloud chamber Molecules of super-saturated air Tiny liquid water drops form
Bubble chamber Molecules of super-saturated liquid hydrogen Tiny hydrogen gas bubbles form
18. 7.7
Particle
detectors
p. 122-123
The diagram on the right shows the spiralling curved track caused by an energetic
electron that entered a bubble chamber from the right.
1. Describe and explain the direction of the magnetic field in the chamber.
2. How can we tell from the diagram that the electron is gradually losing energy and
where is that energy transferred to?
19. 7.8
Einstein’s
equation
p. 124-125
1. Calculate the change in mass of a 65 kg passenger of a car
travelling at a velocity of 30 ms-1
.
2. Calculate the change in mass of a hot cup of 200 g of tea
when it is cooling down from 100 °C to 20 °C. Specific heat
capacity of tea: . Explain the meaning of the negative sign in
your answer.
3. Calculate the mass of an electron moving at a quarter of the
speed of light in a particle accelerator. What went wrong?!
Extension: Suggest why the discovery of the relation between mass and energy was practically
impossible before Einstein.
𝛥 𝐸=𝑐2
𝛥𝑚
According to Einstein’s famous equation, the mass of a particle increases from its rest
mass (the mass it has when at rest), , by when it has extra energy . In the subatomic
world the conservation of mass and the conservation of energy cannot be treated
differently; we rather apply Einstein's principle of conservation of mass-energy.
#5:With the aid of a diagram, show pupils how Rutherford and his team’s experiment cannot prove whether the charge of the nucleus is positive or negative.
