star.le.ac.uk / ~ mbu / lectures.html

1. Lecture course slides can be seen at: • http://www.star.le.ac.uk/~mbu/lectures.html

2. Atomic Spectra Find the photon energy and wavelength for the series limit (shortest wavelength) in the Paschen series (n2 = 3). Calculate the wavelengths for the three longest wavelengths in this series and indicate their positions on a horizontal linear scale.

3. Binding energy What is the binding energy for the hydrogen atom? What is the binding energy for He+? What is the binding energy for Li2+?

4. Ch. 40 Nuclear Physics Radioactivity • Nuclei of one element can transform into another element by radioactive decay • e.g. by emitting photons, electrons, or other particles • a particles are 4He nuclei • b particles are either electrons (b-) or positrons (b+) • g 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

5. Ch. 40 Nuclear Physics Radioactivity Number of nuclei N remaining after time t: where l is the decay constant and N0 is the number of nuclei at t=0 Decay rate R: where R0= lN0= rate of decay at t=0 Average lifetime: Half life:

6. 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 R0 initially: • It will be R0/2 after one half-life • and (1/2)(1/2)R0 = (1/2)2R0 after two half-lives • Therefore, after n half-lives:

7. Radioactive Carbon Dating • An example of b decay: • 14C has a half-life of 5730 yr • Radioactive 14C produced in upper atmosphere by cosmic rays • Like ordinary 12C, combines with O to produce CO2 • Exists in living organisms in a ratio 14C/12C of 1.3x10-12 • When dies, no longer absorbs 14C from atmosphere, and ratio decreases due to radioactive decay of 14C • From half life and no. of 14C 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

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

9. Nuclear reactions • Energy and mass are interchangeable • A nucleus is lighter than the sum of its component nucleons by a quantity DE/c2where DE 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

10. 1.007825 1.008665 2.01102 3.016050 4.002603 6.015125 (1 u)c2 = 931.5 MeV Nuclear reactions Find the Q values for the following reactions: Unified mass units Table 40-1 in Tipler 1u = 1/12th the mass of a 12C atom Rest energy of 1u: