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Chapter 30: Q25CQ (page 1111)
For a given value of n, what are the allowed values of l ?
The allowed values of l are:
\(l = 0,\;1,\;2, \ldots ,\;n - 1\)
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Integrated Concepts
Estimate the density of a nucleus by calculating the density of a proton, taking it to be a sphere1.2 fm in diameter. Compare your result with the value estimated in this chapter.
A beryllium ion with a single electron (denoted ) is in Be3+ an excited state with radius the same as that of the ground state of hydrogen.
(a) What is n for the Be3+ ion?
(b) How much energy in eV is needed to ionize the ion from this excited state?
Look up the values of the quantities in\[{{\bf{a}}_{\bf{B}}}{\bf{ = }}\frac{{{{\bf{h}}^{\bf{2}}}}}{{{\bf{4}}{{\bf{\pi }}^{\bf{2}}}{{\bf{m}}_{\bf{e}}}{\bf{kq}}_{\bf{e}}^{\bf{2}}}}\], and verify that the Bohr radius aB is 0.529 x 10-10 m.
(a) What is the magnitude of the angular momentum for an l = 1 electron?
(b) Calculate the magnitude of the electron鈥檚 spin angular momentum.
(c) What is the ratio of these angular momenta?
Rutherford found the size of the nucleus to be about \({\bf{1}}{{\bf{0}}^{{\bf{ - 15}}}}\;{\bf{m}}\). This implied a huge density. What would this density be for gold?
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