29Exercises
2.1. Find the number of carbon (162C ) atoms in 1 cm3 of graphite, density 1.65 g/cm3.
2.2. Estimate the radius and volume of the gold atom, using the metal density of 19.3 g/cm3 and atomic weight close to 197. Assume that atoms are located at corners of cubes and that the atomic radius is that of a sphere with volume equal to that of a cube.
2.3. Calculate the most probable speed of a "neutron gas" at temperature 20°C (293K), noting that the mass of a neutron is 1.67 x 10-27 kg.
2.4. Prove that the specific heat of an atomic gas is given by cp = (3/2)(k/m), using the formula for average energy of a molecule.
2.5. Calculate the energy in electron volts of a photon of yellow light (see Section 2.3). Recall from Section 1.2 that 1 eV = 1.60 x 10-19 J.
2.6. What frequency of light is emitted when an electron jumps into the smallest orbit of hydrogen, coming from a very large radius (assume infinity)?
2.7. Calculate the energy in electron-volts of the electron orbit in hydrogen for which n = 3, and find the radius in centimeters. How much energy would be needed to cause an electron to go from the innermost orbit to this one? If the electron jumped back, what frequency of light would be observed?
2.8. Sketch the atomic and nuclear structure of carbon-14, noting Z and A values and the numbers of electrons, protons, and neutrons.
2.9. If A nucleons are visualized as spheres of radius r that can be deformed and packed tightly in a nucleus of radius R, show that r = 1.4 x 10-13 cm.
2.10. What is the radius of the nucleus of uranium-238 viewed as a sphere? What is the area of the nucleus, seen from a distance as a circle?
2.11. Find the fraction of the volume that is occupied by the nucleus in the gold-197 atom, using the relationship of radius R to mass number A. Recall from Exercise 2.2 that the radius of the atom is 1.59 x 10- 8 cm.
2.12. Find the binding energy in MeV of ordinary helium, 2 He, for which M = 4.002603.
2.13. How much energy (in MeV) would be required to completely dissociate the uranium-235 nucleus (atomic mass 235.043923) into its component protons and neutrons?
2.14. Find the mass density of the nucleus, the electrons, and the atom of U-235, assuming spherical shapes and the following data:
atomic radius 1.7 x 10-10 m nuclear radius 8.6 x 10-15 m electron radius 2.8 x 10-15 m mass of 1 amu 1.66 x 10-27 kg mass of electron 9.11 x 10-31 kg
Discuss the results.
2.15. Maxwell's formula for the number of molecules per unit speed is n(v) = n0 A v2 exp(-mv2 / 2kT)
where n0 is the total number of molecules and
(a) Verify by differentiation that the peak of the curve is at vp V2 kT / m
(b) Verify by integration that the average speed
is given by
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