Ta có

\(\left.\begin{matrix} \varepsilon _{42}=\frac{hc}{\lambda _{42}}=E_4-E_2\\ \varepsilon _{53}=\frac{hc}{\lambda _{53}}=E_5-E_3 \end{matrix}\right\} \ \frac{\varepsilon _{42}}{\varepsilon _{53}}=\frac{\lambda _{53}} {\lambda _{42}}=\frac{E_4-E_2}{E_5-E_3}\)
\(\Rightarrow \frac{\lambda _{53}}{\lambda _{42}}=\frac{-\frac{13,6}{4^2} -(-\frac{13,6}{2^2})}{-\frac{13,6}{5^2}-(-\frac{13,6}{3^2})}\)
\(\Rightarrow \frac{\lambda _{53}}{\lambda _{42}}=\frac{-\frac{1}{4^2}+\frac{1}{2^2}} {-\frac{1}{5^2}+\frac{1}{3^2}}=\frac{675}{256}\) 

\(\Rightarrow \frac{\lambda _{53}}{\lambda _{42}}=\frac{675}{256}\)