b
\((b)\) Wave length of the electron wave be \(10 \times {10^{ - 12}}m\),

Using \(\lambda = \frac{h}{{\sqrt {2mE} }}\)\( \Rightarrow E = \frac{{{h^2}}}{{{\lambda ^2} \times 2m}}\)

\( = \frac{{{{(6.63 \times {{10}^{ - 34}})}^2}}}{{{{(10 \times {{10}^{ - 12}})}^2} \times 2 \times 9.1 \times {{10}^{ - 31}}}}Joule\)

\( = \frac{{{{(6.63 \times {{10}^{ - 34}})}^2}}}{{{{(10 \times {{10}^{ - 12}})}^2} \times 2 \times 9.1 \times {{10}^{ - 31}} \times 1.6 \times {{10}^{ - 19}}}}eV\)

\(= 15.1\ KeV.\)