PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei l Lecture course slides can be seen at:

PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei Atomic Spectra Find the photon energy and wavelength for the series limit (shortest wavelength) in the Paschen series (n 2 = 3). Calculate the wavelengths for the three longest wavelengths in this series and indicate their positions on a horizontal linear scale.

PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei Binding energy What is the binding energy for the hydrogen atom? What is the binding energy for He + ? What is the binding energy for Li 2+ ?

PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei Ch. 40 Nuclear PhysicsRadioactivity Nuclei of one element can transform into another element by radioactive decay e.g. by emitting photons, electrons, or other particles  particles are 4 He nuclei  particles are either electrons (    or positrons (     rays are photons The rate of decay is a random, statistical process and decreases exponentially over time Impossible to predict when an individual nucleus will decay, only an average time over which an ensemble will characteristic of a process which is quantum mechanical in nature Decay rates are independent of temperature and pressure

PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei Nuclear Physics Radioactivity Ch. 40 Number of nuclei N remaining after time t: where is the decay constant and N 0 is the number of nuclei at t=0 Decay rate R: where R 0 =  = rate of decay at t=0 Half life: Average lifetime:

PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei After each time interval of one half-life: The number of nuclei N remaining has decreased by half The decay rate R has decreased by half For example, if the decay rate is R 0 initially: It will be R 0 /2 after one half-life and (1/2)(1/2)R 0 = (1/2) 2 R 0 after two half-lives Therefore, after n half-lives:

PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei Radioactive Carbon Dating An example of  decay: 14 C has a half-life of 5730 yr Radioactive 14 C produced in upper atmosphere by cosmic rays Like ordinary 12 C, combines with O to produce CO 2 Exists in living organisms in a ratio 14 C/ 12 C of 1.3x When dies, no longer absorbs 14 C from atmosphere, and ratio decreases due to radioactive decay of 14 C From half life and no. of 14 C nuclei in a gram of C, can calculate decay rate of 15 min -1 g -1. From this and measured number of decays per min in a gram of dead organism, can determine its age

PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei Radioactivity A wood sample contains 10 g of carbon and shows a 14 C decay rate of 100 counts/min. How old is it? 14 C has a half-life of 5730 yr and exists in living material in a ratio 14 C/ 12 C of 1.3x10 -12, giving a decay rate of 15 min -1 g -1. What decay rate would you expect from 15 g of 10,000 yr old wood?

PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei Nuclear reactions Energy and mass are interchangeable A nucleus is lighter than the sum of its component nucleons by a quantity  E/c 2 where  is the binding energy The differing binding energies of parent and daughter nuclei during fission and fusion reactions leads to their importance in energy generation (and big explosions!) In the reaction: The mass of the products is less than the inputs, so energy is released. This is quantified by the “Q factor”: If mass of incoming particles > outgoing, energy released, Q positive, reaction is called exothermic If mass of incoming < outgoing, energy absorbed, Q negative, endothermic

PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei Nuclear reactions Find the Q values for the following reactions: (1 u)c 2 = MeV Unified mass units Table 40-1 in Tipler 1u = 1/12 th the mass of a 12 C atom Rest energy of 1u: