Final answer:
The energy required to excite the electron from the ground state to the sixth excited state can be calculated using the formula E = (n^2 * h^2)/(8mL^2), where n is the quantum number, h is Planck's constant, m is the mass of the electron, and L is the length of the box.
Step-by-step explanation:
The energy levels of an electron in a 1D box are given by the equation:
E = (n^2 * h^2)/(8mL^2)
Where E is the energy, n is the quantum number of the energy level, h is Planck's constant, m is the mass of the electron, and L is the length of the box.
Given that the length of the box is 0.1 nm, we can calculate the energy required to excite the electron from the ground state to the sixth excited state:
E_6 - E_1 = ((6^2 * h^2)/(8mL^2)) - ((1^2 * h^2)/(8mL^2))
Substituting the values of h, m, and L, we can solve for the energy difference.