Hydrogen atoms jump between the first eight levels, in every possible way…

Step 1. Which series. A jump that ends on $n = 1$ gives ultraviolet. Jumps that end on $n = 3$ or higher give infrared. So we try $n_f = 2$.

Step 2. The jumps. With $\dfrac{1}{\lambda} = R\left(\dfrac{1}{4} - \dfrac{1}{n_i^2}\right)$:

• $3 \to 2$: $656\ \text{nm}$
• $4 \to 2$: $486\ \text{nm}$
• $5 \to 2$: $434\ \text{nm}$
• $6 \to 2$: $410\ \text{nm}$
• $7 \to 2$: $397\ \text{nm}$, just outside the range.

Step 3. Answer. There are 4 visible lines, from $410\ \text{nm}$ to $656\ \text{nm}$.