# option b: quantum and nuclear physics b2 nuclear physics

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Option B: Quantum and nuclear physics B2 Nuclear physics. B.2.1Explain how the radii of nuclei may be estimated from charged particle scattering experiments. B.2.2Describe how the masses of nuclei may be determined using a Bainbridge mass spectrometer. - PowerPoint PPT Presentation

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• Option B: Quantum and nuclear physicsB2 Nuclear physicsB.2.1Explain how the radii of nuclei may be estimated from charged particle scattering experiments.B.2.2Describe how the masses of nuclei may be determined using a Bainbridge mass spectrometer.B.2.3Describe one piece of evidence for the existence of nuclear energy levels.

• Option B: Quantum and nuclear physicsB2 Nuclear physicsExplain how the radii of nuclei may be estimated from charged particle scattering experiments.As you may recall from Topic 7, Rutherford determined that the bulk of the atoms positive charge (and mass) is located in a very small central nucleus have a radius of about 10-15 m.If we analyze a head-on collision between an alpha particle and a nucleus, we can obtain a rough value for the diameter of a nucleus.A nucleus has a charge of positive Ze and an alpha particle has a charge of positive 2e.As the alpha particle approaches the nucleus it will be slowed down, stopped (for an instant), and reversed by the Coulomb force.FYIReview Topic 7 for much of what is in this option.

• Option B: Quantum and nuclear physicsB2 Nuclear physicsExplain how the radii of nuclei may be estimated from charged particle scattering experiments.

The alpha particle feels a coulomb potential caused by the nucleus given by V = kQ/r or V = kZe/r.If the alpha particle approaches from infinity, the work needed to stop it at rmax is given by W = qV = 2eV = 2kZe2/rmax.From the work-kinetic energy theorem (W = EK) we get W = EK-EK,0. Since at rmax, EK = 0, W = EK,0.

where EK,0 is the initial kinetic energy of the particle.

• Option B: Quantum and nuclear physicsB2 Nuclear physicsEXAMPLE: Alpha particles having a kinetic energy of EK = 5 MeV bombard a gold nucleus and rebound straight back. Estimate the radius of the gold nucleus.

SOLUTION: Gold (Au) has Z = 79. The alpha particles kinetic energy must be converted to joules: EK,0 = (5106 eV)(1.610-19 J/eV) = 810-13 J.Then rmax = 2kZe2/EK,0 = 2(9109)(79)(1.610-19)2/810-13 = 510-14 m.Explain how the radii of nuclei may be estimated from charged particle scattering experiments.Why is the actual radius of the nucleus less than rmax.

• Option B: Quantum and nuclear physicsB2 Nuclear physicsDescribe how the masses of nuclei may be determined using a Bainbridge mass spectrometer.Recall the mass spectrometer in which an atom is stripped of its elec- trons and accelerated through a voltage into a magnetic field.Scientists determined through the use of such a device that hydrogen nuclei came in three different masses:Since the charge of the hydrogen nu-cleus is e, scientists postulated the existence of a neutral particle called the neutron.

• Option B: Quantum and nuclear physicsB2 Nuclear physicsDescribe how the masses of nuclei may be determined using a Bainbridge mass spectrometer.While in the magnetic field the charged particle feels a centripetal force caused by the magnetic field of Fc = qvB sin .But the angle between v and B is 90 so that sin = 1.Since Fc = mv2/r thenmv2/r = qvB so that

• Option B: Quantum and nuclear physicsB2 Nuclear physicsDescribe how the masses of nuclei may be determined using a Bainbridge mass spectrometer.PRACTICE: Track X shows the deflection of a singly-charged carbon-12 ion in the deflection chamber of a mass spectrometer. Which path best shows the deflection of a singly-charged carbon-14 ion? Assume both ions travel at the same speed.SOLUTION: Since carbon-14 is heavier, it will have a bigger radius than carbon-12.Since its mass is NOT twice the mass of carbon-12, it will NOT have twice the radius.

• Option B: Quantum and nuclear physicsB2 Nuclear physicsDescribe how the masses of nuclei may be determined using a Bainbridge mass spectrometer.EXAMPLE: A hydrogen ion (proton) is accelerated through a potential difference of V = 475 V and projected into a mass spectrometer having a magnetic field strength of 0.250 T.(a) What is the velocity of the proton after its acceleration?(b) What is its radius of curvature in the spec?SOLUTION:(a) EK = qV = (1.610-19)(475) = 7.610-17 J.Then 7.610-17 = (1/2)mv2 = (1/2)(1.6710-27)v2 and v = 3.0105 ms-1.(b) r = mv/(qB) = (1.6710-27)(3.0105)/[(1.610-19)(0.250)] = 0.013 m (1.3 cm)

• Option B: Quantum and nuclear physicsB2 Nuclear physicsDescribe one piece of evidence for the existence of nuclear energy levels.Recall that electrons in an atom moving from an excited state to a de-excited state release a photon.The emission spectra of de-exciting atoms show the existence of atomic energy levels.In exactly the same way, de-exciting nuclei also release photons which also produce spectra - only with very high energy photons called gamma rays: 234Pu* 234Pu +

Atomic spectral lines.Nuclear spectral lines.

• Option B: Quantum and nuclear physicsB2 Nuclear physicsRadioactive decayB.2.4Describe beta plus (+) decay including the existence of the neutrino.B.2.5State the radioactive decay law as an exponential function and define the decay constant.B.2.6Derive the relationship between decay constant and half-life.B.2.7Outline methods for measuring the half-life of an isotope.B.2.8Solve problems involving radioactive half-life.

• Option B: Quantum and nuclear physicsB2 Nuclear physicsRadioactive decayDescribe beta plus (+) decay including the existence of the neutrino.There are two types of beta () particle decay:In - decay, a neutron becomes a proton and an electron is emitted from the nucleus. 14C 14N + + e-In + decay, a proton becomes a neutron and a positron is emitted from the nucleus. 10C 10B + + e+In short, a beta particle is either an electron or an anti-electron.-+

• Option B: Quantum and nuclear physicsB2 Nuclear physicsRadioactive decayDescribe beta plus (+) decay including the existence of the neutrino.In contrast to the alpha particle, it was discovered that beta particles could have a large variety of kinetic energies.

In order to conserve energy it was postulated that another particle called a neutrino was created to carry the additional EK needed to balance the energy.Same total energy

• Option B: Quantum and nuclear physicsB2 Nuclear physicsRadioactive decayState the radioactive decay law as an exponential function and define the decay constant.The higher the initial popu- lation of a radioactive ma- terial, the more decays there will be in a time interval.But each decay decreases the population.Hence the decay rate decreases over time for a fixed sample and it is an exponential decrease.

where N0 is the initial population, N is the new one, t is the time, and is the decay constant.Time in half-livesRadioactive material remaining

• Option B: Quantum and nuclear physicsB2 Nuclear physicsRadioactive decayDerive the relationship between decay constant and half-life.EXAMPLE: Show that the relationship between half-life and decay constant is given by T1/2 = ln 2/.SOLUTION: Use N = Noe-t. Then N = N0/2 when t = T1/2. Then N = Noe-t N0/2 = Noe-T (1/2) = e-T ln(1/2) = -T1/2-ln(1/2) = T1/2 ln 2 = T1/2

Exponential decay function.Substitution.Cancel N0.ln x and ex are inverses.Multiply by -1.-ln (1/x) = +ln x.

• Option B: Quantum and nuclear physicsB2 Nuclear physicsRadioactive decaySolve problems involving radioactive half-life.EXAMPLE: The half-life of U-238 is 4.51010 y and for I-123 is 13.3 h. Find the decay constant for each radioactive nuclide. SOLUTION: Use T1/2 = ln 2/. Then = ln 2/T1/2.For U-238 we have = ln 2/T1/2 = 0.693/4.51010 y = 1.510-11 y-1.For I-123 we have = ln 2/T1/2 = 0.693/13.3 h = 0.052 h-1. FYIThe decay constant is the probability of decay of a nucleus per unit time.

• Option B: Quantum and nuclear physicsB2 Nuclear physicsRadioactive decayOutline methods for measuring the half-life of an isotope.Rather than measuring the amount of remaining radioactive nuclide there is in a sample (which is hard to do) we measure instead the decay rate (which is much easier).Decay rates are measured using various devices, most commonly the Geiger-Mueller counter.Decay rates are measured in Becquerels (Bq).

• Option B: Quantum and nuclear physicsB2 Nuclear physicsRadioactive decayOutline methods for measuring the half-life of an isotope.The decay rate A is given by

The N is the change in the number of nuclei, and is negative (the radioactive sample loses population with each decay).The negative sign is in A = -N/t to make the activity A positive.A = N shows that the activity is proportional to the remaining population of radioactive nuclei, which we learned in Topic 7. Since N = Noe-t the last equation A = Noe-t is true.

• Option B: Quantum and nuclear physicsB2 Nuclear physicsPRACTICE: Radioactive decaySolve problems involving radioactive half-life.Rem