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- Suppose you are designing a proton decay experiment and you can detect 50 percent of the proton decays in a tank of water. (a) How many kilograms of water would you need to see one decay per month, assuming a lifetime of 1031 y? (b) How many cubic meters of water is this? (c) If the actual lifetime is 1033 y, how long would you have to wait on an average to see a single proton decay?A nuclear physicist finds 1.0of 236Uin a piece of uranium ore (T1/2=2.348107y) . (a) Use die decay law to determine how much 236Uwould had to have been on Earth when it formed 4.543109yago for 1.0gto be left today, (b) What is unreasonable about this result? (c) How is this unreasonable result resolved?12) How much material is left when you start with 22.5-g and you have gone through 4.84 half-lives?
- U-235 sphere the size of a Tootsie Pop Assume that a spherical volume of pure U-235 is the size of a Tootsie Pop. The per capita electrical energy usage (i.e., per person per year) in the U.S. is 11,496 kw-hrs a) How many years would this amount of U-235 power the average person if all the U-235 atoms were fissioned? b) What would be the approximate volume of the waste produced, when the entire sample has fissioned? (Describe this qualitatively.) Assumptions to use: • Pop diameter = 1.25 inch • Density of the U-235 sample = 18.95 g/cc . The atomic mass is 235.044 amu • 180 MeV of heat energy are available from each fission . The efficiency for thermal to electric conversion is 0.32 . Avogadro's number = 6.022e23.When U-232 undergoes alpha decay to Th-228, a mass lost is sustained. 1. Find the mass defect for this process in amu and kg. 2. The mass lost during the decay is converted to kinetic energy. Use Einstein equation to calculate the kinetic energy in joules and in Mega- electron volts (MeV). The exact mass of U-232 is 232.0372 amu. The exact mass of Th-228 is 228.0287 amu. The exact mass of He is 4.0026 amu. 1 amu= 1.6606 x 10-27 kg. 1 MeV = 1.602 x 10-13 J. 232 92 U -----> 228 90 Th + 4 2 He i have a attached a photo of the question.d) The equation below describes the disintegration of a bismuth nucleus into a thallium nucleus and an alpha-particle. During the reaction energy Q is released. 212 208 Bi He + 83 81 TI + energy released Q. The masses in the atomic mass unit u are as follows: 212 83 208 Bi = 211.99127 u, 81 TI = 207.98201 u and He = 4.002050 u. You may assume that 1u is equivalent to 931 MeV. Calculate: i) The loss of mass during the reaction. ii) kinetic energy of the products. e) When an alpha particle is emitted, the thallium nucleus recoils in the opposite direction. Use the principle of the conservation of momentum to estimate how the kinetic energy will be shared between the thallium nucleus and the a- particle.
- Page No. Date Thys 101-02 If a Fourth particle of mass 2.00kis Placed at X= 9 Y= O.200m Find the X- and the C.g. Coordingtes oF SHOT ON MI9T Al TRIPLE CAMERAB. Carbon-14 is a radioactive isotope of carbon that has a half-life of 5600 years. It is used extensively in dating organic material that is tens of thousands of years old. Model the differential equation of the decay of the isotope if m is the mass and t is the time Calculate the constant using the half-life time. What fraction of the original amount of Carbon-14 in a sample would be present after 10,000 years? i) ii)-Write an expression for the conservation of momentum in the y direction, taking upwards as positive. -Write the correct equation from below for θTh. -Find the numerical value of θTh in degrees. You may assume that the mass of these particles is the number of nucleons (4 or 238) times the mass of a proton, 1.673 × 10-27 kg. -Write an expression for the speed of the thorium nucleus in terms of sin(θTh).
- 19) What is the amount of starting material when 0.35-g remain and the number of half-lives is 2.72 R S=A sample of protactinium-234 of mass 100 g has a half-life of 6.7 hours.A. What fraction of the sample has not decayed after 20.1 hours?B. What is the mass of undecayed protactinium-234 after this period of time?The radioactive gas krypton-85, produced by nuclear power plants as well as volcanoes, is present in trace amounts in earth’s atmosphere. Its half-life is 10.8 years. Suppose a volcano released 250 g of krypton-85 in an eruption. How much would remain after (a) 10.8 years, (b) 15 years, and (c) 50 years? Round to the nearest tenth of a gram.