Answer
$E = 13.6~eV$
Work Step by Step
According to Equation (39-33):
$E_n = \frac{me^4}{8\epsilon_0^2h^2}~\frac{1}{n^2}$
We can verify that the combined value of the constants is $13.6~eV$:
$E = \frac{me^4}{8\epsilon_0^2h^2}$
$E = \frac{(9.109\times 10^{-31}~kg)(1.6\times 10^{-19}~C)^4}{(8)(8.854\times 10^{-12}~F/m)^2(6.626\times 10^{-34}~J~s)^2}$
$E = 2.1681\times 10^{-18}~J$
$E = (2.1681\times 10^{-18}~J)(\frac{1~eV}{1.6\times 10^{-19}~J})$
$E = 13.6~eV$
