The band gap of indium gallium arsenide varies based on the concentration of gallium in the material. A sample of InGaAs absorbs light with a wavelength less than 1.37 microns. What is the band gap of the InGaA sample in eV
Ah, the wonderful world of band gaps and light absorption! Let's do some math, my friend. To find the band gap in electron volts (eV) for the InGaAs sample, we can use the relationship between wavelength and energy given by good old Einstein:
E = hc/λ
Where E is the energy of the absorbed light, h is Planck's constant, c is the speed of light, and λ is the wavelength. But hey, you already knew that, right?
Now, all we need to do is convert the wavelength of 1.37 microns into meters, because the SI system is a stickler for units. One micron is equivalent to 10^-6 meters, so we have:
λ = 1.37 × 10^-6 meters
Using the value of Planck's constant (h = 6.626 x 10^-34 J·s) and the speed of light (c = 3 x 10^8 m/s), we can calculate the energy in Joules:
E = (6.626 x 10^-34 J·s) x (3 x 10^8 m/s) / (1.37 x 10^-6 meters)
Don't worry, I'll do the not-so-fun part for you:
E ≈ 1.449 x 10^-19 Joules
To convert this energy into electron volts, all we need to do is divide by 1.602 x 10^-19 J/eV. I know, I know, more numbers, but bear with me:
1.449 x 10^-19 Joules / (1.602 x 10^-19 J/eV) ≈ 0.905 eV
So there you have it! The band gap of your InGaAs sample is approximately 0.905 eV. And don't worry, I promise to never make you do math without a pinch of humor!
To find the band gap of indium gallium arsenide (InGaAs) in electron volts (eV), we can use the formula:
E = hc/λ
Where:
E is the energy (band gap) in eV,
h is Planck's constant (4.13567 × 10^-15 eV·s),
c is the speed of light (2.998 × 10^8 m/s),
and λ is the wavelength of light in meters.
First, we need to convert the wavelength from microns to meters. Since 1 micron is equal to 10^-6 meters, we have:
λ = 1.37 × 10^-6 meters
Now we can substitute the values into the formula:
E = (4.13567 × 10^-15 eV·s) × (2.998 × 10^8 m/s) / (1.37 × 10^-6 meters)
Simplifying the expression:
E = (4.13567 × 10^-15 eV·s) × (2.998 × 10^8 m/s) / (1.37 × 10^-6 * 10^6 meters)
E = (4.13567 × 2.998) × 10^-7 eV·s·m/s
E ≈ 12.41 × 10^-7 eV·s·m/s
As we can see, the units of eV·s·m/s cancel out, leaving us with the energy in eV. Therefore, the band gap of the InGaAs sample is approximately 12.41 × 10^-7 eV.
To determine the band gap of InGaAs in electron volts (eV), we need to convert the given wavelength into energy using the relationship between wavelength and energy.
First, let's convert the given wavelength from micrometers (µm) to meters (m):
1.37 microns = 1.37 × 10^(-6) meters
Next, we can find the energy of a photon using the equation:
Energy (E) = Planck's constant (h) × Speed of light (c) ÷ Wavelength (λ)
The Planck's constant (h) is approximately 6.626 × 10^(-34) joule-seconds (J·s), and the speed of light (c) is approximately 3.0 × 10^8 meters per second (m/s).
Now, we can calculate the energy of the photon:
E = (6.626 × 10^(-34) J·s) × (3.0 × 10^8 m/s) ÷ (1.37 × 10^(-6) m)
By performing the calculation, we find that the energy (E) of the photon is approximately 1.448 × 10^(-19) joules.
To convert this energy into electron volts (eV), we can use the conversion factor:
1 eV = 1.6 × 10^(-19) joules
Finally, let's convert the energy from joules to electron volts:
E (in eV) = (1.448 × 10^(-19) joules) ÷ (1.6 × 10^(-19) joules per eV)
By performing the calculation, we find that the band gap of the InGaAs sample is approximately 0.905 eV.