Nuclear engineering is all about harnessing the energy that is released by reactions within atoms. This energy can be used for a variety of things, including generating electricity, powering transportation systems, and diagnosing and treating illnesses. One of the most common places to find nuclear engineers at work is in a nuclear power plant. While nuclear engineers are central to the design, construction and maintenance of power plants, they are also responsible for proper safety procedures and disposal of nuclear waste. Nuclear engineers can also be found in other fields, where they might develop radioactive medicines such as radiation therapy that treats cancers, or design power sources for space satellites or equipment on the moon, etc.

At the heart of a nuclear power plant is a nuclear reactor, which contains and controls the reactions that occur within the atoms. These reactions produce heat, which is used to boil water to make steam. The steam is then used to turn a turbine and generate electricity.

4.1 Nuclear reactors are powered by uranium fuel, which consists of small pellets packaged into long, metal tubes called fuel rods. These fuel rods are then organized into fuel assemblies, each of which is made up of 264 fuel rods. Assume 137 fuel assemblies are needed to fuel a nuclear reactor. If each pellet weighs 10 g, and there are 250 pellets in each fuel rod, what is the total weight, in kilograms, of the uranium fuel inside a fully loaded reactor?

4.2 Nuclear power plants produce radioactive waste, which can be dangerous for the environment if it is not disposed of correctly. Often radioactive waste from nuclear power plants is disposed of underground in special storage facilities. In these storage facilities, a high-powered HVAC (heating, ventilation and air conditioning) system is required to keep the air pressure inside the facility lower than the air pressure outside the facility. This ensures that the radioactive material remains inside the facility and does not flow out into the environment.

The HVAC system in a particular nuclear waste storage facility has 10 fans. There must be 7 or more of these fans running to maintain the low air pressure in the facility. How many different combinations of one or more fans can be broken at the same time without causing radioactive material to escape the storage facility?

4.3 Technetium-99m, or 99mTe, is an isotope (a radioactive form of an element) that is used in nuclear medicine to determine how certain parts of a person’s body, particularly their bones, heart muscle or brain, are functioning. The half-life of 99mTe (or rather, the amount of time it takes for a quantity of 99mTe to decay and be reduced by half) is six hours. If a hospital needs to receive 50 g of 99mTe for its medical procedures, and it takes exactly 48 hours from its production to reach the hospital, how many grams of 99mTe must be shipped to the hospital? Express your answer in scientific notation to three significant figures.

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