33 \times 10^{-7}$ m
**Step 2:**
For the second member of the Lyman series with $n=3$:
Given formula: $\frac{1}{\lambda} = R(\frac{1}{1^2} - \frac{1}{3^2})$
Substitute the values: $\frac{1}{\lambda} = R(\frac{1}{1} - \frac{1}{9})$
Solve for $\lambda$: $\lambda =
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