Chapter 31 - Atomic Physics - Conceptual Questions - Page 1111: 9

Please see the work below.

We know that $E_n=\frac{-13.6eV}{n^2}$ We plug in $n=1$ to obtain: $E1=-\frac{-13.6eV}{(1)^2}=-13.6eV$ Now for $n=\infty$, we obtain: $E_{\infty}=\frac{-13.6}{(\infty)^2}=0eV$ Thus, the energy does not increases without limit. The energy of a given level in a hydrogen atom ranges from the lower limit $-13.6eV$ to the upper limit $0$.