Low energy nuclear reactions can be studied by accelerating ions with a tandem van de Graaff accelerator. The accelerator consists of a positive high voltage terminal and a stripper foil in the middle of the accelerator. Low energy (~keV) negative ions (such as He-, for example) are injected in the accelerator from a negative ion source. These ions are attracted and accelerated towards the positive terminal in the center. When passing through the stripper foil they are converted into positive ions (say, He ). Now they are repelled from the terminal and accelerated even more (~MeV). After the accelerator typically a magnet bends the beam of interest onto a target, where the nuclear reactions occur and can be studied.
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(a) What is the effective resistance (in ohms) between the terminal and ground when the terminal held at 18.3 MV results in a current of 53.0 mA between the terminal and the ground.
(b) Assume a 9Be- ion is injected into the accelerator with the terminal voltage V_T at 18.3 MV and then it is stripped of some of its electrons to form 9Be . What is its final kinetic energy, in MeV, when it leaves the tandem accelerator.
(c) This ion is bent through a radius of 1.3m after the accelerator. How large is the magnetic field (in Tesla) of the bending magnet ? (Mass(9Be) = 9 u)
(d) After the bend the 9Be collides and fuses with a 14N target nucleus to form 23Na. What is the recoil kinetic energy of the 23Na nucleus in MeV? (Mass(23Na) = 23 u). Here use conservation of momentum (not energy) to find the recoil velocity and then calculate the recoil kinetic energy.
(e) If the 9Be collides with a 27Si target and the particles do not fuse but one reaction product is a 1H, what is the Z of the other resulting reaction product?
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