To calculate the energy levels and wavelengths of photons emitted or absorbed by an electron in a one-dimensional box, we can use the formula for the energy levels in a particle in a box:

E_n = (n^2 * h^2) / (8 * m * L^2)

Where:
E_n is the energy level of the electron
n is the quantum number (1, 2, 3, ...)
h is the Planck's constant (6.62607015 × 10^-34 J·s)
m is the mass of the electron (9.10938356 × 10^-31 kg)
L is the length of the one-dimensional box (0.1 nm)

Let's calculate the energy levels:

For n = 1:
E_1 = (1^2 * h^2) / (8 * m * L^2)

For n = 2:
E_2 = (2^2 * h^2) / (8 * m * L^2)

And so on...

To calculate the corresponding wavelengths, we can use the formula:

λ = c / f

Where:
λ is the wavelength of the photon
c is the speed of light in a vacuum (2.998 × 10^8 m/s)
f is the frequency of the photon, which can be calculated from the energy using the equation:

E = hf

Where:
E is the energy of the photon
h is the Planck's constant (6.62607015 × 10^-34 J·s)

Let's plug in the values and calculate:

For n = 1:
E_1 = (1^2 * (6.62607015 × 10^-34 J·s)^2) / (8 * (9.10938356 × 10^-31 kg) * (0.1 × 10^-9 m)^2)

λ_1 = (2.998 × 10^8 m/s) / ((Plugged in value of E_1 / 6.62607015 × 10^-34 J·s))

For n = 2:
E_2 = (2^2 * (6.62607015 × 10^-34 J·s)^2) / (8 * (9.10938356 × 10^-31 kg) * (0.1 × 10^-9 m)^2)

λ_2 = (2.998 × 10^8 m/s) / ((Plugged in value of E_2 / 6.62607015 × 10^-34 J·s))

And so on...

By plugging in the values of n into the formulas, you can calculate the energy levels and wavelengths for each energy level of the electron in the one-dimensional box.

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