The treatment of a particle in a one-dimensional box can be extended to a two-dimensional box of dimensions L _ { x }L x and L _ { y }L y yielding the following expression for energy: E = \frac { h ^ { 2 } } { 8 m } \left( \frac { n _ { x } ^ { 2 } } { L _ { x } ^ { 2 } } + \frac { n _ { y } ^ { 2 } } { L _ { y } ^ { 2 } } \right)E= 8mh 2( L x2n x2+ L y2n y2)The two quantum numbers independently can assume only integer values. Consider an electron confined to a two-dimensional box that is 8.00 nm in the x direction and 5.00 nm in the y direction. a. What are the quantum numbers for the first three allowed energy levels? b. Calculate the wavelength of light necessary to promote an electron from the first excited state to the second excited state.