Assume a hydrogen atom is a sphere with diameter 0.100 nm and a hydrogen molecule consists of two such spheres in contact. (a) What fraction of the space in a tank of hydrogen gas at 08C and 1.00 atm is occupied by the hydrogen molecules themselves? (b) What fraction of the space within one hydrogen atom is occupied by its nucleus, of radius 1.20 fm

Assume a hydrogen atom is a sphere with diameter 0.100 nm and a hydrogen molecule consists of two such spheres in contact. (a) What fraction of the space in a tank of hydrogen gas at 08C and 1.00 atm is occupied by the hydrogen molecules themselves? (b) What fraction of the space within one hydrogen atom is occupied by its nucleus, of radius 1.20 fm

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter31: Radioactivity And Nuclear Physics

Section: Chapter Questions

Problem 14PE: (a) Show that if you assume the average nucleus is spherical with a radius r=r0A1/3, and with a mass...

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Assume a hydrogen atom is a sphere with diameter 0.100 nm and a hydrogen molecule consists of two such spheres in contact. (a) What fraction of the space in a tank of hydrogen gas at 0°C and 1.00 atm is occupied by the hydrogen molecules themselves? (b) What fraction of the space within one hydrogen atom is occupied by its nucleus, of radius 1.20 fm?
A particle of ionizing radiation creates 4,600 ion pairs in the gas inside a Geiger tube as it passes through. What minimum energy (in J) was deposited, if 21.0 eV is required to create each ion pair? If all of this energy is converted to thermal energy in the gas, what is its temperature increase (in K), assuming 55.0 cm3 of ideal gas at 0.300 atm pressure? (The small answer is consistent with the fact that the energy is large on a quantum mechanical scale but small on a macroscopic scale. Assume the initial temperature of the gas is 293 K.)
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(a) Show that if you assume the average nucleus is spherical with a radius r=r0A1/3, and with a mass at A u, then its density is independent at A. (b) Calculate that density in u/fm3 and kg/m3, and compare your results with those found in Example 31.1 for 56Fe.
Calculate (a) the thermal wavelength, (b) the translational partition function of an Ar atom in a cubic box of side 1.00 cm at (i) 300 K and (ii) 3000 K.
The brightest star in the sky is Sirius, the Dog Star. Itis actually a binary system of two stars, the smaller one (Sirius B)being a white dwarf. Spectral analysis of Sirius B indicates that itssurface temperature is 24 000 K and that it radiates energy at a totalrate of 1.0 · 1025 W. Assume that it behaves like an ideal blackbody.(a) What is the radius of Sirius B? Express your answer in kilometersand as a fraction of our Sun’s radius (R= 6.96 · 108 m). (b) Whichstar radiates more total energy per second, the hot Sirius B or the(relatively) cool Sun with a surface temperature of T = 5800 K? Tofind out, calculate the ratio of the total power radiated by our Sun tothe power radiated by Sirius B.
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 10-27 kg.Densities of Some Common Substances at Standard Temperature (0°C) and Pressure (Atmospheric) Substance ρ (kg/m3) Substance ρ (kg/m3) Air 1.29 Iron 7.86 ✕ 103 Air (at 20°C andatmospheric pressure) 1.20 Lead 11.3 ✕ 103 Aluminum 2.70 ✕ 103 Mercury 13.6 ✕ 103 Benzene 0.879 ✕ 103 Nitrogen gas 1.25 Brass 8.4 ✕ 103 Oak 0.710 ✕ 103 Copper 8.92 ✕ 103 Osmium 22.6 ✕ 103 Ethyl alcohol 0.806 ✕ 103 Oxygen gas 1.43 Fresh water 1.00 ✕ 103 Pine 0.373 ✕ 103 Glycerin 1.26 ✕ 103 Platinum 21.4 ✕ 103 Gold 19.3 ✕ 103 Seawater 1.03 ✕ 103 Helium gas 1.79 ✕ 10−1 Silver 10.5 ✕ 103 Hydrogen gas 8.99 ✕ 10−2 Tin 7.30 ✕ 103 Ice 0.917 ✕ 103 Uranium 19.1 ✕ 103 (a) Determine the density of the proton.kg/m3
< V hat is the fraction of alpha particle scattering with angles 0°, more than 1°, and more than 90° respectively? (a) 0.0125%, 0.14%, and 99.86% (b) 0.14%, 0.0125%, and 99.86% (¢) 99.86%, 0.14%, and 0.0125% (d) None of the above
In the planetary model of the atom where electrons orbit a centralized nucleus, what is the approximate ratio of the radius of the nucleus to that of the electron orbits?
I need to calculate the volume of a water droplet using V=4/3(3.14)r^3 with a radius of 0.025mm. I get 6.54498469. Am I on the right track?
(b) Calculate the half width in nanometers for Doppler broadening of the 4s S 4p transition for atomic nickel at 361.939 nm (3619.39 Å) at a temperature of 20,000 K in both wavelength and frequency units. (e) Calculate the speed that an iron atom undergoing the 4s S 4p transition at 385.9911 nm (3859.911 Å) would have if the resulting line appeared at the rest wavelength for the same transition in nickel. (f) Compute the fraction of a sample of iron atoms at 10,000 K that would have the velocity calculatedin (e). (g) Create a spreadsheet to calculate the Doppler half width DlD in nanometers for the nickel and iron lines cited in (b) and (e) from 3000–10,000 K. (h) Consult the paper by Gornushkin et al. (note 10) and list the four sources of pressure broadening that they describe. Explain in detail how two of these sources originate in sample atoms.
Calculate the turning point of an alpha particle (Z =2) directed with initial kinetic energy of 2.0 MeV, if the trajectory of the alpha particle was headed directly toward a single gold nucleus (Z =79) (the nuclei in the gold foil in Rutherford’s experiment). How close could the alpha particle in Rutherford’s experiment get to the center of a gold nucleus?