What is the minimum wavelength of light that can promote an electron from the valence band to the conduction band in silicon?
Here is a site that lists the energy gap between the valence band and the conduction band.
http://www-inst.eecs.berkeley.edu/~ee130/fa07/lectures/Semiconductor_fundamentals_lec1.pdf
For Si that is 1.12 eV. convert that to wavelength.
1 eV = 1.6 x 10^-19 joules and
E = hc/lambda
Plug in 1 eV (in joules) for E, h is Planck's constant, c is the speed of light at 3.0 x 10^8 m/s, and lambda is what you calculate. Post your work if you get stuck.
To determine the minimum wavelength of light that can promote an electron from the valence band to the conduction band in silicon, we need to consider the energy gap between the two bands.
In silicon, the energy gap between the valence band and the conduction band is known as the bandgap energy. The bandgap energy for silicon is approximately 1.1 electron volts (eV).
To convert this energy into wavelength, we can use the equation:
E = (hc) / λ
Where:
E is the energy in joules,
h is Planck's constant (6.62607015×10^-34 J·s),
c is the speed of light (2.998 × 10^8 m/s), and
λ is the wavelength in meters.
First, let's convert the bandgap energy from electron volts (eV) to joules (J):
1 eV = 1.60218 × 10^-19 J
So, the bandgap energy for silicon is:
E = 1.1 eV * (1.60218 × 10^-19 J/eV)
E ≈ 1.7634 × 10^-19 J
Next, we can rearrange the equation to solve for wavelength (λ):
λ = (hc) / E
Substituting the values, we get:
λ = (6.62607015 × 10^-34 J·s * 2.998 × 10^8 m/s) / (1.7634 × 10^-19 J)
λ ≈ 3.5452 x 10^-7 meters
Therefore, the minimum wavelength of light that can promote an electron from the valence band to the conduction band in silicon is approximately 3.5452 x 10^-7 meters, or about 354.52 nanometers.
To find the minimum wavelength of light that can promote an electron from the valence band to the conduction band in silicon, we need to understand the bandgap energy of silicon and the relation between energy and wavelength.
The bandgap energy is the minimum energy required to promote an electron from the valence band to the conduction band in a material. For silicon, the bandgap energy is approximately 1.1 electronvolts (eV).
Now, we can use the relation between energy and wavelength given by the equation:
E = hc/λ
where E is the energy, h is Planck's constant (6.626 x 10^-34 kg m^2/s), c is the speed of light (3 x 10^8 m/s), and λ is the wavelength.
To find the minimum wavelength, we need to convert the bandgap energy from electronvolts to joules and substitute it into the equation.
1 eV is approximately 1.6 x 10^-19 joules.
Substituting the values into the equation:
1.1 eV = (6.626 x 10^-34 kg m^2/s)(3 x 10^8 m/s) / λ
Rearranging the equation to solve for wavelength:
λ = (6.626 x 10^-34 kg m^2/s)(3 x 10^8 m/s) / (1.1 eV)(1.6 x 10^-19 J/eV)
Calculating the value, we get:
λ ≈ 1.12946 x 10^-6 meters
Therefore, the minimum wavelength of light that can promote an electron from the valence band to the conduction band in silicon is approximately 1.12946 micrometers (µm).