Final answer:
The energy of the state nx = 2, ny = 4 in an infinitely deep rectangular well with sides of length Lx=L and Ly=2L is h^2/(2*m*L^2).
Step-by-step explanation:
To find the energy of a state nx = 2, ny = 4 in an infinitely deep rectangular well with sides of length Lx=L and Ly=2L, we use the formula for the allowed energies of an electron in a box, which is given by the equation E = (nx^2*h^2)/(8*m*L^2) + (ny^2*h^2)/(32*m*L^2), where h is the Planck constant and m is the mass of the electron.
Substituting nx = 2 and ny = 4, the energy of the state can be calculated as E = (2^2*h^2)/(8*m*L^2) + (4^2*h^2)/(32*m*L^2). Simplifying this expression, we get E = h^2/(2*m*L^2) + h^2/(2*m*L^2), which simplifies to E = 2*h^2/(2*m*L^2), and further simplifies to E = h^2/(m*L^2).
Therefore, the correct option is (c) h^2/(2*m*L^2).