b
\(\lambda=\frac{{h}}{{mv}}=\frac{{h}}{\sqrt{2 {mE}}}, {mv}=\sqrt{2 {mE}}\)

\(\lambda \propto \frac{1}{\sqrt{{E}}}\) \(\frac{\lambda_{2}}{\lambda_{1}}=\sqrt{\frac{{E}_{1}}{{E}_{2}}}=\frac{3}{4}, \lambda_{2}=0.75 \lambda_{1}\)

\(\frac{{E}_{1}}{{E}_{2}}=\left(\frac{3}{4}\right)^{2}\)

\({E}_{2}=\frac{16}{9} {E}_{1}=\frac{16}{9} {E} \quad\left({E}_{1}={E}\right)\)

Extra energy given \(=\frac{16}{9} {E}-{E}=\frac{7}{9} {E}\)