An electron falls from the conduction band of silicon (Si) to the valence band. The band gap of Si is 1.1 eV. What is the wavelength of the photon emitted by this process? Give your answer in nm.

1129 nm

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To determine the wavelength of the photon emitted when an electron falls from the conduction band to the valence band in silicon, we can use the relationship between energy, wavelength, and the speed of light.

1. First, let's convert the energy from electronvolts (eV) to joules (J), since the units need to be consistent.

We know that 1 eV is equal to 1.602 x 10^-19 J (the elementary charge, e, is 1.602 x 10^-19 C).

Therefore, the energy of the photon emitted is 1.1 eV * (1.602 x 10^-19 J/eV) = 1.763 x 10^-19 J.

2. Next, let's use the relationship between energy (E), wavelength (λ), and the speed of light (c):

E = hc/λ

where h is Planck's constant (6.626 x 10^-34 J·s) and c is the speed of light (2.998 x 10^8 m/s).

Rearranging the equation, we get:

λ = hc/E

3. Plugging in the values:

λ = (6.626 x 10^-34 J·s * 2.998 x 10^8 m/s) / (1.763 x 10^-19 J)

λ ≈ 3.56 x 10^-7 m

4. Finally, let's convert the wavelength from meters (m) to nanometers (nm) by multiplying by 10^9:

λ = 3.56 x 10^-7 m * 10^9 nm/m ≈ 356 nm

Therefore, the wavelength of the photon emitted when an electron falls from the conduction band to the valence band in silicon is approximately 356 nm.