Por favor me ajudem,se possível ainda hoje!

Para esse exercício, realizaremos os cálculos abaixo:

\(\begin{align} & \text{a)} \\ & {{\text{E}}_{\text{c}}}\text{ }\!\!~\!\!\text{ = 1/2}{{\text{m}}_{\text{e}}}{{\text{v}}^{\text{2}}}\text{ }\!\!~\!\!\text{ } \\ & {{\text{E}}_{\text{c}}}\text{ }\!\!~\!\!\text{ = h}{{\text{f}}_{\text{2}}}\text{ }\!\!~\!\!\text{ }\!\!~\!\!\text{ }\!\!~\!\!\text{ }\!\!~\!\!\text{ } \\ & \text{logo }{{\text{E}}_{\text{c}}}\text{ }\!\!~\!\!\text{ = 1/2 }\!\!\times\!\!\text{ 9}\text{,1x 1}{{\text{0}}^{\text{-3}}}^{\text{1}}\text{kg }\!\!\times\!\!\text{ (3}\text{,6 x 1}{{\text{0}}^{\text{6}}}\text{ }\!\!~\!\!\text{ m}\text{.}{{\text{s}}^{\text{-1}}}{{\text{)}}^{\text{2}}}\text{ }\!\!~\!\!\text{ } \\ & \text{ hc/}{{\text{l}}_{\text{2}}}\text{ }\!\!~\!\!\text{ = }\left( \text{6}\text{,626 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-34}}} \right)\text{ }\!\!\times\!\!\text{ }\left( \text{2}\text{,998 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{8}}} \right)\text{ }\!\!~\!\!\text{ /}{{\text{l}}_{\text{2}}}\text{ }\!\!~\!\!\text{ } \\ & \text{ }{{\text{l}}_{\text{2}}}\text{ }\!\!~\!\!\text{ = 1}\text{,99 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-25}}}\text{ }\!\!~\!\!\text{ / 5}\text{,87 x 1}{{\text{0}}^{\text{-18}}} \\ & \text{ }{{\text{l}}_{\text{2}}}\text{ }\!\!~\!\!\text{ = 3}\text{,39 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-8}}}\text{ }\!\!~\!\!\text{ m} \\ & \\ & \text{b)} \\ & \text{ }\!\!~\!\!\text{ }{{\text{f}}_{\text{1}}}\text{ }\!\!~\!\!\text{ = 2}\text{,50 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{16}}} \\ & \text{ }{{\text{E}}_{\text{i}}}\text{ }\!\!~\!\!\text{ = f = h}{{\text{f}}_{\text{1}}} \\ & \text{ h}{{\text{f}}_{\text{1}}}\text{ }\!\!~\!\!\text{ = 6}\text{,626 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-34}}}\text{ }\!\!~\!\!\text{ }\!\!\times\!\!\text{ }\left( \text{ 2}\text{,50 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{16}}}\text{ }\!\!~\!\!\text{ } \right) \\ & \text{ h}{{\text{f}}_{\text{1}}}\text{ }\!\!~\!\!\text{ = 1}\text{,66 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-17}}}\text{ }\!\!~\!\!\text{ J} \\ & \\ & \text{c)} \\ & \text{h}{{\text{f}}_{\text{2}}}\text{ }\!\!~\!\!\text{ = hf -- h}{{\text{f}}_{\text{1}}} \\ & \text{ hf = h}{{\text{f}}_{\text{2}}}\text{ }\!\!~\!\!\text{ + h}{{\text{f}}_{\text{1}}}\text{ }\!\!~\!\!\text{ } \\ & \text{hf= 5}\text{,87 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-18}}}\text{ }\!\!~\!\!\text{ + }\!\!~\!\!\text{ 1}\text{,66 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-17}}}\text{ }\!\!~\!\!\text{ } \\ & \text{hf= 2}\text{,23 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-17}}}\text{ }\!\!~\!\!\text{ J }\!\!~\!\!\text{ } \\ & \\ & \begin{array}{*{35}{l}} \begin{align} & \text{hf = hc/l = 2}\text{,23 x 1}{{\text{0}}^{\text{-17}}}\text{ }\!\!~\!\!\text{ } \\ & \text{6}\text{,626 }\!\!\times\!\!\text{ x 1}{{\text{0}}^{\text{-34}}}\text{ }\!\!~\!\!\text{ }\left( \text{ 2}\text{,998 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{8}}} \right)\text{/l = 2}\text{,23 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-17}}}\text{ }\!\!~\!\!\text{ } \\ & \text{ l = 1}\text{,99 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-25}}}\text{ }\!\!~\!\!\text{ m/2}\text{,23 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-17}}} \\ & \text{l = 8}\text{,92 nm} \\ \end{align} \\ {} \\ \end{array} \\ \end{align}\ \)