PhysicsLAB AP Free Response Question
1999 B4

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You use a Geiger counter to measure the decay of a radioactive sample of bismuth 212 over a period of time and obtain the following results.

Time (min)            0     20     40    60     80   100   120   140   160   180   200
Counts/minute    702   582   423   320   298   209   164   154   124     81    79
(a) Your results are plotted on the following graph. On the graph, draw an estimate of a best-fit curve that shows the radioactive counts as a function of time.

 (b) From the data or from your graph, determine the half-life of this isotope. Explain how you arrived at your answer.

The bismuth isotope decays into thallium by emitting an alpha particle according to the following equation:
212 83Bi → Tl + α
(c) Determine the atomic number Z and the mass number A of the thallium nuclei produced and enter your answers in the spaces provided below.


(d) The mass of the alpha particle is 6.64 x 10-27 kg. Its measured kinetic energy is 6.09 MeV where 1 eV = 1.6 x 10-19 J and its speed is much less than the speed of light.
 i. Determine the momentum of the alpha particle.

 ii. Determine the kinetic energy of the recoiling thallium nucleus.

 (e) Determine the total energy released during the decay of one mole of bismuth 212.

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