Physics 2: Physical Science & Technology (PHYC10004)
Week 12
Discussion Questions
1
Discuss the structure of the atom briefly, including
• an order of magnitude estimate of the size ofthe atom and its nucleus
• a comparison of the forces involved in the stability of the atom and the nucleus, including the range, strength and particles involved.
2
Over what range does the strong nuclear force play a significant role? How is this force important in explaining why the “line of stability” in elements is non-linear, i.e. why there are more neutrons in heavier elements than protons?
3
Explain the meaning of binding energy.
4
Explain the difference between fission and fusion, indicating the relevance of the graph below.
5
Wolfgang Pauli was led to suggest the existence of the neutrino long before its discovery, by a puzzle about the energy and momentum of the products of beta decay. What was this puzzle? Also, how did Fermi know that the neutrino should be a neutral particle?
Problem-solving Questions
6
a) Explain what is meant by the Heisenberg Uncertainty Principle
In the Bohr model, an electron in the ground state of a hydrogen atom is considered to have a kinetic energy of 13.6 eV.
b) Show that the momentum of this electron is approximately 2 × 10-24 kg. ms-1.
c) Use the Uncertainty Principle to estimate the diameter of the hydrogen atom.
7
We wish to measure the wavelength and position of a photon simultaneously. The wavelength of the photon is 600 nm and is known with an accuracy What is the minimum uncertainty in the position of the photon?
8
The following table gives the charge seen by Millikan at different times on single oil drops in his experiment. From the data, calculate the elementary charge e.
Halliday, David. Fundamentals of Physics Extended, 10th Edition. John Wiley & Sons,
9
The radioactive isotope undergoes beta (–) and beta (+) decay. Write the equation for both of these decays. Include the relevant neutrinos.
10
Another form of ‘beta decay’ is known as electron capture. In this process, an inner shell electron is ‘captured’ by the nucleus, with the resulting ejection of a neutrino from the nucleus. Find the isotope of the element labelled ‘X’ in the equation below:
11
A typical nuclear fission reaction of U-235 has the equation:
• Find the isotope of Barium formed.
• the reaction above liberates ~ 175 MeV of energy. If 1 mole of U-235 fissions like this, estimate the amount of energy released, & compare it to the energy output of a 1 GW power station.
Past examination questions
12
If the half-life for a radioactive nuclide is known, one can in principle use this to measure large time intervals. 40K is one such element, decaying to 40Ar with a half-life of 1.25×109 years.
Analysis of moon rock samples reveals that the ratio of stable 40Ar to the radioactive 40K is 10:1.
a) Assuming that at formation of the rock there were N0 atoms of 40K, and zero atoms of 40Ar, show that
where t is the time since the formation of the rock, and λ is the disintegration constant.
b) Use the relationship in (a) to determine the approximate age of the moon rock.
13
Listed below are some of the elements of the actinide series of the periodic table.
All of these are radioactive, and apart from uranium none are found naturally occurring in any significant qualities on Earth. In contrast, the isotope is found in abundance.
a) What can you infer about the half-life of in comparison with the age of the Earth?
Of the synthetically produced actinides, the isotope Americium is the only one to have made its way into our homes where it is commonly used in smoke detectors. Most is produced as a by-product of the nuclear fission cycle by decay of the radioactive element .
b) What type of decay produces from ?
A smoke detector o contained 1.000 µg of americium when it was manufactured 30 years ago. The americium is also radioactive and decays by alpha particle emission with a half- life of 432.2 years.
c) Calculate the mass of that remains in the smoke detector today.
d) Re-write the equation below by specifying the values ofA and Z and identifying element X, to correctly reflect the radioactive decay of americium.
14
The nuclear reactor at ANSTO creates the isotope Mo-99 which then decays to the metastable isotope Tc-99m. The Tc-99m is used as a radioactive tracer for helping to determine the cause of a patient’s illness. The Tc-99m tracer emits a gamma ray during its decay to Tc-99. Tc-99 then further decays to Ru-99 which is a stable isotope.
The decay series and relevant information for each isotope is given in the table below;
(a) The Molybdenum is transported to hospitals and produces the metastable Technetium to be injected into the patient.
(i) Mo-99 decays to the metastable Tc-99m via beta decay. Write the decay equation and justify whether the decay is β- or β+.
(ii) Show that the energy released during this decay is 1.216 MeV.
(b) Ruthenium is the only stable atom in the decay series. Determine the binding energy per nucleon of Ru-99.