An electron is confined to an infinite one-dimensional potential well in which its ground-state (n = 1) energy is measured to be 1.1 eV.What is the length L of the well in units of nm?Answer for part 1 What energy input (in eV) is required to promote the electron to its first excited state?

The energy levels of an electron in a one-dimensional infinite potential well are given by the equation:

E_n = n²h² / (8mL²)

where:

• E_n is the energy of the level n,
• h is the Planck constant,
• m is the mass of the electron,
• L is the width of the well.

Given that the ground state energy E_1 is 1.1 eV, we can rearrange the equation to solve for L:

L = sqrt(n²h² / (8mE_n))

Substituting the known values (n = 1, h = 4.1357 x 10^-15 eV.s, m = 9.10938356 x 10^-31 kg, E_1 = 1.1 eV), we get:

L = sqrt((1² * (4.1357 x 10^-15 eV.s)²) / (8 * 9.10938356 x 10^-31 kg * 1.1 eV)) L = 4.83 x 10^-9 m = 4.83 nm

For the second part of the question, the energy required to promote the electron to its first excited state (n = 2) is simply the difference between the energy of the first excited state and the ground state:

E_2 - E_1 = 2²/1² * E_1 - E_1 = 3 * E_1 = 3 * 1.1 eV = 3.3 eV.