Questions on nuclear fusion & fission reactions (HL)

1. The nucleus of an atom of uranium-235 consists of 92 protons and 143 neutrons.

(a) Use Section 4 of the data booklet to determine the total mass (in kg) of 92 protons, and 143 neutrons.

(b) The nuclear mass of uranium-235 is 235.043924 g mol^-1. Calculate the binding energy of uranium-235 in kJ mol^-1.
(Avogadro’s constant = 6.022142 × 10²³ mol^-1; velocity of light = 2.997925 x 10⁸ m s^-1)

(c) Uranium-235 can react with one neutron in a nuclear reaction to form krypton-90, barium-144 and two neutrons. The total nuclear mass of the products from this reaction when one mole of uranium-235 reacts completely is 235.8454 g.
Calculate the total theoretical amount of energy that 1 mol of uranium can produce in this reaction.

2. (a) Show how Graham’s law of effusion can be deduced from the relationship between temperature and kinetic energy.

(b) Deduce the relative molar mass of a gas that effuses 1.37 times faster than ethane.

(c) Calculate how much faster hydrogen will escape through a small hole in a container compared to nitrogen.

3. Strontium-90 is present in spent nuclear fuel and in radioactive waste from nuclear reactors and also as fallout from nuclear tests. It is a beta-emitter. The following graph shows the decay of 100 g of strontium-90 over a period of 144 years.

(a) Deduce the nuclear equation for the decay of strontium-90

(b) Explain how the graph demonstrates that the radioactive decay of strontium-90 is kinetically a first order process.

(c) Calculate the mass of strontium-90 remaining after 200 years.

(d) Suggest why strontium-90 is a particularly hazardous radioactive isotope to humans.

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