\(E_1=\frac{h c}{\lambda_1}=-w_0 \quad \text { or } \quad \frac{1}{2} m_e V^2=\frac{h c}{\lambda_1}-w_0\)

\(E_2=\frac{h c}{\lambda_2}-w_0 \quad \text { or } \quad \frac{1}{2} m_e 4 V^2=\frac{h c}{\lambda_2}-w_0\)

\(\frac{1}{4}=\frac{h c}{\lambda_1}-w_0\)

\(\frac{h c}{\lambda_2}-w_0\)

\(\frac{h c}{\lambda_2}-w_0=\frac{4 h c}{\lambda_1}-4 w_0\)

\(3 w_0=\frac{4 h c}{\lambda_1}-\frac{h c}{\lambda_2}\)

\(w_0=\frac{12400}{3}\left(\frac{4}{\lambda_1}-\frac{1}{\lambda_2}\right)\)

\(w_0=2 \,eV\)