Answer
See answers.
Work Step by Step
a. Boron has 4 protons, Z = 4. Use the Bohr model.
$$E_2=-\frac{(13.6 eV)(Z_{eff}^2)}{n^2}$$
$$-8.26eV=-\frac{(13.6 eV)(Z_{eff}^2)}{2^2}$$
$$Z_{eff}=1.56$$
The other electron in the n = 2 shell partially shields the nucleus from this n = 2 electron.
b. Use equation 27-14 to find the average radius.
$$r=\frac{n^2 r_1}{ Z_{eff}}=\frac{2^2 (0.529\times10^{-10}m)}{1.56}=1.36\times10^{-10}m $$
