Phys 115 1st Edition Lecture 24Outline of Last Lecture I. Nuclear structureII. Nuclear stabilityIII. Forces and energy in the nucleusIV. Radiation and radioactivityV. Nuclear decay and half-livesOutline of Current Lecture I. Radiation and radioactivityII. Nuclear decay and half-livesIII. Nuclear physics in medicineCurrent Lecture- Nuclear Decay and Half-Liveso The number of nuclei N remaining at time t is given by: o The decay of radioactive nuclei is an exponential decay.o The equation for the number of atoms after a half-life can be written in terms of a time constant τ that is related to the half-life:- Classroom Response Question 1o Patients with Graves disease have an overactive thyroid gland. A common treatment uses radioactive iodine, which is taken up by the thyroid. The radiationemitted in its decay will damage the tissues of the gland. A single pill is produced with 4.0  1014 atoms of the isotope 131I, which has a half-life of 8.0 days.o Although the iodine in the pill is constantly decaying, it is still usable as long as it contains at least 2.5  1014131I atoms. What is the maximum delay before the pill is no longer usable?- Classroom Response Question 2o A sample contains radioactive atoms of two types, A and B. Initially there are fivetimes as many A atoms as there are B atoms. Two hours later, the numbers of the two atoms are equal. The half-life of A is 0.50 hours.o Is the half-life of B greater than, less than, or equal to that of A?o After two hours, what fraction of A is remaining? - ActivityThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.o The activity of a radioactive sample is the number of decays per second. Each decay corresponds to an alpha, beta, or gamma emission.o The activity of a sample N nuclei with a time constant τ or half life t½ iso We can find the variation of activity with time: o N0/τ is the initial activity R0 so the decay of activity is o The SI unit of activity is the becquerel:o 1 becquerel = 1 Bq = 1 decay/second o The curie is also usedo 1 curie = 1 Ci = 3.7 x 1010Bq- Classroom Response Question 3 o40K (t1/2 = 1.3  109yr) and 14C (t1/2 = 5.7  103yr) are two radioactive isotopes found in measurable quantities in your body. Suppose you have 20 g of 40K and 14g of 14C. Which is more radioactive—that is, which has a greater activity?o A: Potassiumo B: Carbon- Nuclear Physics in Medicineo The energies of the alpha and beta particles and gamma-ray photons of nuclear decay are typically in the range 0.1 – 10 MeV. These energies are much higher than the ionization energies of atoms and molecules (~few eV).o Very large doses of ionizing radiation can break bonds and lead to cell death.o In the treatment of brain tumors, gamma-ray photons are concentrated on the tumor with the use of a collimator.o Other tumors are treated by surgically implanting low-energy radioactive “seeds within a tumor.o Some tissues preferentially take up certain isotopes, allowing treatment by isotope ingestion. A common treatment for hyperthyroidism is to damage the gland with isotope 131I, resulting in a reduction of the gland’s activity with minimal disruption of surrounding tissue.- Doseo The biological effects of radiation depend on how much energy was absorbed by the body and how tissue reacts to different forms of radiation.o We define the radiation dose as the energy from ionizing radiation absorbed by 1kg of tissue.o The SI unit of a dose is the gray, abbreviated Gy.o 1 Gy = 1.00 J/kg of absorbed energy.o Relative Biological Effectivenesso The relative biological effectiveness (RBE) is defined as the biological effect of a given dose relative to the biological effect of an equal dose of x-rays.o The radiation dose equivalent is the product of the energy dose in Gy and the relative biological effectiveness. It is measured in sieverts, Sv.- Dose equivalent in Sv = dose in Gy x RBE.- Additional Unitso Doses may be given in rad and dose equivalents in rem. The conversions are shown below.- Classroom Response Question 4o A patient receives a gamma scan of his liver. He ingests 3.7 MBq of 198Au, which decays with a 2.7 day half-life by emitting a 1.4 MeV beta particle. Medical tests show that 60% of this isotope is absorbed and retained by the liver, what is the total dose equivalent received by a patient’s 1.5 kg liver once all of the atoms have decayed?- Nuclear Imagingo Nuclear imaging uses radiation from isotopes from within the body to produce an image of the tissues in the body.o The use of gamma-emitting 99Tc with a gamma-ray camera, can to detect areas where active growth is occurring.o The image produced by a gamma ray camera highlights areas of active