Answer
See answers.
Work Step by Step
Use equation 27–14 to solve for the radius of the n = 1 orbit when Z = 92. The radius is inversely proportional to the atomic number.
$$r_n=\frac{n^2}{Z}(0.529\times10^{-10}m)= \frac{1^2}{92}(0.529\times10^{-10}m)= 5.75\times10^{-13}m $$
To estimate the energy required to remove that innermost electron, estimate the electron’s energy (which will be negative as it is in a bound state). The energy required to remove it is the magnitude of that energy, because when the electron is free, it has E = 0.
Use equation 27–15b. The energy of the electron in a Bohr orbit is proportional to the square of the atomic number. Use Z = 92, because the innermost electron is not shielded from the 92 protons in the nucleus.
$$|E_n|=(13.6eV) \frac{Z^2}{n^2}=(13.6eV) \frac{92^2}{1^2}=1.15\times10^5 eV$$
It would take about 115 keV to remove the innermost electron of a uranium atom.
