COLLEGE PHYSICS
2nd Edition
ISBN: 9781464196393
Author: Freedman
Publisher: MAC HIGHER
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Chapter 27, Problem 28QAP
To determine
The density of an atomic nucleus compared to the density of an atom.
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In an alpha particle scattering experiment, it is determined that the ratio of the cross-sectional area of the target nucleus to that of the atom is 3.25 x 10-9. Determine the radius of the nucleus (in m), if the radius of the atom is 2.25 x 10-10 m.
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Chapter 27 Solutions
COLLEGE PHYSICS
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- Determine the number of neutrons in a bromine nucleus, which has a radius of approximately 5.32 ✕ 10−15 m.arrow_forward•3 @ A thermal neutron (with approximately zero kinetic energy) is absorbed by a 23U nucleus. How much energy is transferred from mass energy to the resulting oscillation of the nucleus? Here are some atomic masses and the neutron mass. 237U 237.048 723 u 239U 239.054 287 u 238U 238.050 782 u 240U 240.056 585 u 1.008 664 uarrow_forward*•58 Two radioactive materials that alpha decay, 238U and 232Th, and one that beta decays, "K, are sufficiently abundant in granite to contribute significantly to the heating of Earth through the de- cay energy produced. The alpha-decay isotopes give rise to decay chains that stop when stable lead isotopes are formed. The isotope 4"K has a single beta decay. (Assume this is the only possible decay of that isotope.) Here is the information: Stable Decay Half-Life End Parent Mode (y) Point (MeV) (ppm) 238U 232Th 4.47 x 10° 206рЬ 51.7 1.41 x 1010 208Pb 42.7 13 1.28 x 10° 40Ca 1.31 4 In the table Q is the total energy released in the decay of one par- ent nucleus to the final stable end point and f is the abundance of the isotope in kilograms per kilogram of granite; ppm means parts per million. (a) Show that these materials produce energy as heat at the rate of 1.0 x 10-9 W for each kilogram of granite. (b) Assuming that there is 2.7 x 102 kg of granite in a 20-km-thick spherical shell at…arrow_forward
- •49 SSM Generally, more massive nuclides tend to be more un- stable to alpha decay. For example, the most stable isotope of ura- nium, 28U, has an alpha decay half-life of 4.5 x 10° y. The most stable isotope of plutonium is 24Pu with an 8.0 x 10' y half-life, and for curium we have 248Cm and 3.4 x 10 y. When half of an original sam- ple of 238U has decayed, what fraction of the original sample of (a) plu- tonium and (b) curium is left?arrow_forwardNuclear Physics - Nuclear Structure Density= Nuclear Structure Z mass Volume radius r=r04¹/3 ro=1.2x10-¹5 m N A = Z+N 4 The radius r of a nucleus is given in the above figure. The volume of a nucleus is V = Proton 56 Fe nucleus has a total of 56 nucleons (protons + neutrons). The average mass of a nucleon is u = 1.66x10^-27 kg I whin ber Neutron A Z If this unknown nucleus has 60 neutrons, how many protons does it have? Enter a number rr³ (a)Calculate the radius of a 56 Fe nucleus. Write the radius in fm, 1 fm = 10-15 m. Keep 2 decimal places. Enter a number x10-¹5m, fm (b) Calculate the Denisity of a 56Fe nucleus.. Write the result in terms of 1017 kg/m³. Keep 2 decimal places. Enter a number x10¹7kg/m³ () (c) An unknown hacieus has twice the volume of 56Fe. What is the mass number A of this nucleus? Enter a number iarrow_forwardConstruct Your Own Problem Consider the decay of radioactive substances in the Earth's interior. The energy emitted is converted to thermal energy that reaches the earth's surface and is radiated away into cold dark space. Construct a problem in which you estimate the activity in a cubic meter of earth rock? And then calculate the power generated. Calculate how much power must cross each square meter of the Earth’s surface if the power is dissipated at the same rate as it is generated. Among the things to consider are the activity per cubic meter, the energy per decay, and the size of the Earth.arrow_forward
- 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_forwardHow many kilograms of water are needed to obtain the 198.8 mol of deuterium, assuming that deuterium is 0.01500% (by number) of natural hydrogen?arrow_forwardThe mass (M) and the radius (r) of a nucleus can be expressed in terms of the mass number, A. (a) Show that the density of a nucleus is independent of A (b) Calculate the density of a gold (Au) nucleus. Compare your answer to that for iron (Fe).arrow_forward
- 2 Nuclear Density Nuclear matter is extremely dense. (a) Calculate the density, in kg/m³, of A neutrons in a sphere of radius r = ro A¹/3, where ro = 1.2 x 10-15 m. (b) Find the diameter of a sphere of nuclear matter that would have the same mass as the earth. The average radius of the earth is 6.4 x 106 m and the average density of the earth is 5.5 x 10³ kg/m³.arrow_forward3) Assume that this room was filled with a gas of oxygen molecules O₂ in thermal equilibrium at 0 °C. There are 8 protons and 8 neutrons in the nucleus of an oxygen atom O. You may take the masses of the proton and the neutron to be the same, and ignore the mass of the electrons. 1 atm=1.01x105 N/m², h=1.05x10-34 J-s, mp=1.67x10-27 kg, ka=1.38x10-23 J/K. a) What would the (particle) number density, n, be according to the ideal gas law? b) Compare the number density with the quantum concentration, no, at the same temperature. Is the gas in the classical or quantum regime?arrow_forward12) Compute the approximate nuclear radius of germanium (A = 70)arrow_forward
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