IB Physics Energy of Capacitors

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A tutorial sheet of problems on the HL topic energy of capacitors is given below.

  1. A capacitor gains a charge Q when it is connected by wires to a battery of emf V and zero internal resistance. Is the work done by the battery equal to the energy stored in the capacitor?
  2. A charged capacitor of capacitance C is connected by wires to an uncharged capacitor of equal capacitance. Show that one half of the original energy is lost. Where does it go?
  3. A capacitance C holds a charge Q and is connected in series with a resistance R. What is the heat energy released in R as the capacitor discharges?
  4. A dielectric slab is placed between the plates of a parallel plate capacitor. Explain the change in energy of the capacitor if the slab is inserted keeping (i) the potential difference between the plates constant, (ii) the charge on the plates constant.
  5. See Physics Education, vol 5, p 33, Sep 1998

IB Physics Half-life

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A tutorial sheet on the terms decay constant, mean lifetime and half-life is given below.

  1. Is the mean lifetime of a particle the same as the half-life of a sample? [No]
  2. Show that mean lifetime of a nucleus = 1/λ, where λ is the decay constant.
  3. Show that half-life of a sample = ln2/λ.
  4. What is the definition of half-life of a sample?
  5. Is the decay constant equal to the probability of a nucleus decaying?
  6. The mean lifetime of a muon is 2.2 μs. Show that the half-life of a sample of muons is 1.52 μs.
  7. A large number of dice are thrown and the die showing a 6 are removed on each throw. A graph is drawn showing the number of remaining dice versus throw number. Show that the decay constant is 1/6 and the half-life is 6ln2 throws.
  8. Radioactive decay is a spontaneous, random process. Define each term.
  9. Two samples of the same element have a different mass. How do the half-lifes of the samples compare?
  10. Why is the half-life constant as a material decays?
  11. A sample of half-life T1 decays into a material of half-life T2. How many daughter nuclei are present when N parent nuclei have decayed?
  12. When a nucleus undergoes beta decay the daughter nucleus has the same number of nucleons as the parent nucleus but the atomic number increases or decreases by 1. True or false?
  13. In the alpha decay of a nucleus the change in binding energy appears as the kinetic energy of the alpha particle and the daughter nucleus. Since the products have equal but opposite momenta the alpha particle has a much greater kinetic energy than the daughter nucleus. True or false?
  14. Gamma decay occurs very often after alpha or beta decay which leaves the daughter nucleus in an excited state. The excess energy is released as a photon from the nucleus. The mass of the excited nucleus is greater than that of the ground state nucleus.True or false?
  15. See P.Dunne et.al, Physics Education, Measurement of the mean lifetime of cosmic ray muons in the A level laboratory, 33, Number 5, 1998.