Hydrogen's light comes from jumps between fixed energy levels, as in The Bohr Model. Each jump gives out (or takes in) one photon, so each pair of levels gives one line in the spectrum. Each problem here is one short scene and a chain of questions. Answer them in order: each later question uses what you found before, so a slip early on carries through. Keep full precision between steps and round only at the end.
Key idea
$$E_n = -\frac{13.6\ \text{eV}}{n^2}, \qquad E_{\text{photon}} = E_{\text{upper}} - E_{\text{lower}}, \qquad \lambda = \frac{1240\ \text{eV·nm}}{E_{\text{photon}}}.$$ Visible light runs from about 400 to 700 nm. Atoms excited to level $N$ can give $N(N - 1)/2$ different lines.
Worked example: From 3 to 2
Find the energy and wavelength of the photon from hydrogen's $n = 3 \to 2$ jump.
- $E_3 = -1.51\ \text{eV}$, $E_2 = -3.40\ \text{eV}$, so $E = 1.89\ \text{eV}$.
- $\lambda = 1240/1.89 = 656\ \text{nm}$: red, visible light.
Answer: $1.89\ \text{eV}$, $656\ \text{nm}$
Common mistake
Using one level's energy as the photon's energy. The photon carries the difference between two levels. Check: a jump between neighboring high levels must give a small energy, and a long wavelength.