Foundations of Astronomy (MindTap Course List)
14th Edition
ISBN: 9781337399920
Author: Michael A. Seeds, Dana Backman
Publisher: Cengage Learning
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Chapter 7, Problem 5RQ
To determine
The number of electron for neutral Helium-3 and the nature of Helium-3 and the reason.
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Assume that a room at sea level is filled with a gas of nitrogen molecules N2
in thermal equilibrium at -10.0 °C (negative ten degrees Celsius). There are 7 protons and 7
neutrons in the nucleus of a nitrogen atom N. 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, kB = 1.38x10-23 J/K .
a) What is the (particle) number density n according to the ideal gas law?
b) Compare the number density n with the quantum concentration ng at the same
temperature.
c) Is the gas in the classical or quantum regime?
It may be argued on theoretical grounds that the radius of the hydrogen atom should depend only on the fundamental constants h, e, the electrostatic force constant k = 1/4πℰ0, and m (the electron’s mass). Use dimensional analysis to show that the combination of these factors that yields a result with dimensions of length is h2kme2.
A proton, which is the nucleus of a hydrogen atom, can be modeled as a sphere with a diameter of 2.4 fm and a mass of 1.67 x 10-27 kg. (a) Determine the density of the proton. (b) State how your answer to part (a) compares with the density of osmium, given in Table 14.1.
Chapter 7 Solutions
Foundations of Astronomy (MindTap Course List)
Ch. 7 - Prob. 1RQCh. 7 - Prob. 2RQCh. 7 - Prob. 3RQCh. 7 - Prob. 4RQCh. 7 - Prob. 5RQCh. 7 - Prob. 6RQCh. 7 - Prob. 7RQCh. 7 - Prob. 8RQCh. 7 - Prob. 9RQCh. 7 - Prob. 10RQ
Ch. 7 - Prob. 11RQCh. 7 - Prob. 12RQCh. 7 - Prob. 13RQCh. 7 - Prob. 14RQCh. 7 - Prob. 15RQCh. 7 - Prob. 16RQCh. 7 - How is heat different from temperature?Ch. 7 - Prob. 18RQCh. 7 - Prob. 19RQCh. 7 - Prob. 20RQCh. 7 - Prob. 21RQCh. 7 - Prob. 22RQCh. 7 - Could an object be orbiting another object and we...Ch. 7 - Prob. 24RQCh. 7 - How Do We Know? How is the macroscopic world you...Ch. 7 - Prob. 1PCh. 7 - Answer these questions for celestial bodies at...Ch. 7 - Prob. 3PCh. 7 - Prob. 4PCh. 7 - Prob. 5PCh. 7 - Prob. 6PCh. 7 - Prob. 7PCh. 7 - Prob. 8PCh. 7 - Prob. 9PCh. 7 - Prob. 10PCh. 7 - Prob. 11PCh. 7 - Prob. 12PCh. 7 - Prob. 1SOPCh. 7 - Prob. 2SOPCh. 7 - Prob. 1LTLCh. 7 - Prob. 2LTLCh. 7 - Prob. 3LTLCh. 7 - Prob. 4LTLCh. 7 - Prob. 5LTLCh. 7 - Prob. 6LTLCh. 7 - Prob. 7LTL
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- In symmetric fission, the nucleus of uranium (238U) splits into two nuclei of palladium (119Pd). The uranium nucleus is spherical with a radius of 7.4×10−15m. Assume that the two palladium nuclei adopt a spherical shape immediately after fission; at this instant, the configuration is as shown in the figure attached. The size of the nuclei in the figure can be calculated from the size of the uranium nucleus because the nucleus material maintains a constant density (the initial nuclear volume equals the final nuclear volume). a) Calculate the electric energy of the uranium nucleus before fission. b) Calculate the total electric energy of the palladium nuclei in the configuration shown in the figure, immediately after fission. Take into account the mutual electric potential energy of the two nuclei and also the individual electric energies of the two palladium nuclei by themselves. c) Calculate the total electric energy a long time after fission when the two palladium nuclei have moved…arrow_forwardA hydrogen atom can be considered as having a central pointlike proton of positive charge e and an electron of negative charge -e that is distributed about the proton according to the volume charge density r = A exp(-2r/a0). Here A is a constant, a0 = 0.53 *10-10 m, and r is the distance from the center of the atom. (a) Using the fact that the hydrogen is electrically neutral, find A. Then find the (b) magnitude and (c) direction of the atom’s electric field at a0.arrow_forwardIn symmetric fission, the nucleus of uranium (238U) splits into two nuclei of palladium (119Pd). The uranium nucleus is spherical with a radius of 7.4×10−15m. Assume that the two palladium nuclei adopt a spherical shape immediately after fission; at this instant, the configuration is as shown in the figure attached. The size of the nuclei in the figure can be calculated from the size of the uranium nucleus because the nucleus material maintains a constant density (the initial nuclear volume equals the final nuclear volume). a) Calculate the electric energy of the uranium nucleus before fission. b) Calculate the total electric energy of the palladium nuclei in the configuration shown in the figure, immediately after fission. Take into account the mutual electric potential energy of the two nuclei and also the individual electric energies of the two palladium nuclei by themselves. c) Calculate the total electric energy a long time after fission when the two palladium nuclei have moved…arrow_forward
- Assume the electron in a hydrogen atom is 53.0 pm from the nucleus of the atom, which consists of a single proton. (a) calculate the electrical force between the electron and the nucleus. (b) Calculate the gravitational force between the electron and the nucleus. (c) What is the ratio of the gravitational force to the electrical force?arrow_forwardSuppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius ra has a charge of +Q, while the outer cylinder of radius rh has charge -Q. srb The electric field E at a radial distance r from the central axis is given by the function: E = ge/d0 + B/r + bo where alpha (a)., beta (8), ao and bo are constants. Find an expression for its capacitance. First, let us derive the potential difference Voh between the two conductors. The potential difference is related to the electric field by: Edr = - Edr Calculating the antiderivative or indefinite integral, Vab = (-aageao + B + bo By definition, the capacitance Cis related to the charge and potential difference by: C = Evaluating with the upper and lower limits of integration for Vab, then simplifying: C = Q/( (e""b/ao - eTala0) + ß In ) + bo (arrow_forwardThe nucleus of a certain atom has a radius of 4.0 × 10^-15 m. An electron orbits the nucleus at a radius of 1.5 × 10^-10 m. Imagine the electron orbit is on the surface of a sphere and that the shape of the nucleus is spherical. Approximately how many nuclei would fit into the sphere on which the electron orbits?arrow_forward
- Below about 80 K the specific heat at constant volume for hydrogen gas (H2) is 3/2 k per molecule, but at higher temperatures the specific heat increases to 5/2 k per molecule. What is the distance between the hydrogen nuclei?arrow_forwardConsider the element Hydrogen. In this atom, assume the electron travels with a speed of 6.8 105 m/s. What is the radius between the nucleus and the orbiting electron in m?arrow_forwardWhat fraction of the total volume of an iceberg is exposed above the surface of the ocean? DATA for the densities of sea ice and water: Use these values to 4 significant figures: 919.0 kg/m^3 and 1033 kg/m^3 A: 0.0469 OB: 0.0530 OC: 0.0599 OD: 0.0677 OE: 0.0765 OF: 0.0864 OG: 0.0977 OH: 0.1104arrow_forward
- Before the neutron was discovered, the only possible constitution of a nucleus with a given (A,Z) was A protons and (A-Z) electrons, leaving a net charge of +Ze. Early indications were that the nitrogen nucleus (A = 14,Z = 7) had a total angular mo- mentum that was an integral multiple of ħ. Is this consistent with a nucleus made of A protons and A-Z electrons? How does the inclusion of neutrons change things?arrow_forwardIn a simple model of a hydrogen atom, the single electron orbits the single proton (the nucleus) in a circular path. Calculate (a) the electric potential set up by the proton at the orbital radius of 52.9 pm, (b) the electric potential energy of the atom, and (c) the kinetic energy of the electron. (d) How much energy is required to ionize the atom (that is, to remove the electron to an infinite distance with no kinetic energy)? Give the energies in electron-volts.arrow_forwardThe two nuclei in the carbon monoxide (CO) molecules are 0.1128 nm apart. The mass of the carbon atom is 1.993x10-26 kg. The mass of the oxygen atom is 2.656x10-26 kg. What is the first excited rotational energy level for the CO molecule? (Give the your answer in meV.)arrow_forward
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