EBK PHYSICS FOR SCIENTISTS & ENGINEERS
5th Edition
ISBN: 9780134296074
Author: GIANCOLI
Publisher: VST
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Chapter 42, Problem 66GP
To determine
Find the ratio of speeds of molecules of gas containing
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Natural uranium is 0.7200% 235U and 99.27% 238U. What were the percentages of 235U and 238℃ in natural uranium when Earth
formed 4.5 x 109 years ago, respectively?
percentage 235U
percentage 238U
%
%
In naturally occurring uranium atoms, 99.3%are 238U 1atomic mass = 238 u, where u = 1.6605 * 10-27 kg2 andonly 0.7% are 235U 1atomic mass = 235 u2. Uranium-fueled reactors require an enhanced proportion of 235U. Since both isotopesof uranium have identical chemical properties, they can be separated only by methods that depend on their differing masses. Onesuch method is gaseous diffusion, in which uranium hexafluoride1UF62 gas diffuses through a series of porous barriers. The lighter 235UF6 molecules have a slightly higher rms speed at a given temperature than the heavier 238UF6 molecules, and this allows thetwo isotopes to be separated. Find the ratio of the rms speeds ofthe two isotopes at 23.0 °C.
On absorption of a single neutron, plutonium Pu-239 can undergo fission into xenon Xe-134 plus
zirconium Zr-103 plus three neutrons. The masses of these nuclei are, mpu-239 = 239.052 amu,
mxe-134 = 133.905 amu, and mzr-103 = 102.927 amu. Calculate the energy given off in this nuclear
reaction.
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- 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?arrow_forward238 U has a natural abundance of 99.3% and 235 U has an abundance of 0.7%. It is the rarer 235 U that is needed for nuclear reactors. The isotopes are separated by forming uranium *UF6 and diffuses slightly faster. Many repetitions of this procedure gradually Uranium has two naturally occurring isotopes. 235 238 hexafluoride UF6, which is a gas, then allowing it to diffuse through a series of porous membranes. UF6 has a slightly larger rms speed than 235 UF6 to that of 238 UF6? separate the two isotopes. What is the ratio of the rms speed of Express your answer to five significant figures. ΑΣφ ?arrow_forwardYou have a 2.8 mol pure sample of an unknown material. After 4.7 h, you discover that 89% has decayed. Determine the half-life, decay constant, mean life, determine what the decay rate is at 4.7 h.arrow_forward
- Identify the conserved quantities in the following processes. A° + u- + v. (c) K- + p → £° +n (a) E- (b) Kg → 27° (d) 2° → A° + y (e) et + e- -→ µt + µ (f) p +n → A + E- (g) Which reactions cannot occur? Why not?arrow_forwardLarge amounts of depleted uranium (238U ) are available as a by-product of uranium processing for reactor fuel and weapons. Uranium is very dense and makes good counter weights for aircraft. Suppose you have a 4000-kg block of 238U . Do you think you could detect this as heat? Explain.arrow_forwardHow many grams of radium can form by passing 235 C through an electrolytic cell containing a molten radium salt?arrow_forward
- Radioactive element AA can decay to either element BB or element CC.The decay depends on chance, but the ratio of the resulting number of BB atoms to the resulting number of CC atoms is always 2/1.The decay has a half-life of 8.00 days.We start with a sample of pure AA. How long must we wait until the number of CC atoms is 1.50 times the number of AAatoms?arrow_forwardA sample of spruce wood taken from Two Creeks forest bed near Milwaukee, Wisconsin, is believed to date from the time of one of the last advances of the continental ice sheet into the United States. The ratio of 14C to 12C in the sample was found to be 0.2446 of the atmospheric value of this ratio. What is the daughter-to-parent ratio for the decay process in the sample? What is the estimated age of the spruce wood sample? Show calculations that support your answer.arrow_forwardAnother series of nuclear reactions that can produce energy in the interior of stars is the carbon cycle first proposed by Hans Bethe in 1939, leading to his Nobel Prize in Physics in 1967. This cycle is most efficient when the central temperature in a star is above 1.6 x 107 K. Because the temperature at the center of the Sun is only 1.5 x 107 K, the following cycle produces less than 10% of the Sun’s energy. (a) A high-energy proton is absorbed by 12C. Another nucleus, A, is produced in the reaction, along with a gamma ray. Identify nucleus A. (b) Nucleus A decays through positron emission to form nucleus B. Identify nucleus B. (c) Nucleus B absorbs a proton to produce nucleus C and a gamma ray. Identify nucleus C. (d) Nucleus C absorbs a proton to produce nucleus D and a gamma ray. Identify nucleus D. (e) Nucleus D decays through positron emission to produce nucleus E. Identify nucleus E. (f) Nucleus E absorbs a proton to produce nucleus F plus an alpha particle. Identify nucleus F.…arrow_forward
- 4.3 The radioactive cobalt isotope, Co, has an half-life of 63 months and undergoes decay. The molar mass of 6°Co is 59.9338222 amu. A sample initially contains 48 mg of 6°Co. (a) Calculate the number of moles of 6Co that are left in the sample after 5.0 years. (b) Calculate the activity of 60CO after 5.0 years, in units of per month (month).arrow_forwardProblem 2: Nuclear fusion - the energy source of the Sun, hydrogen bombs, and fusion reactors - occurs much more readily when the average kinetic energy of the nuclei is high. P A Suppose you want the nuclei in your fusion experiment to have average kinetic energies of 5.5 x 10-14 J. What temperature, in kelvins, is needed for that? T= sin() cos() tan() HOME E AL *1| 2 cotan() asin() acos) 4 5 atan() acotan() sinh() cosh() tanh() cotanh() + - END ODegrees O Radians Vol BACKSPACE DEL CLEAR Submit Hint Feedback I give up! Farrow_forward(a) Estimate the years that the deuterium fuel in the oceans could supply the energy needs of the world. Assume world energy consumption to be ten times that of the United States which is 8×1019 J/y and that the deuterium in the oceans could be converted to energy with an efficiency of 32%. You must estimate or look up the amount of water in the oceans and take the deuterium content to be 0.015% of natural hydrogen to find the mass of deuterium available. Note that approximate energy yield of deuterium is 3.37×1014 J/kg. (b) Comment on how much time this is by any human measure. (It is not an unreasonable result, only an impressive one.)arrow_forward
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