Question

The energy band gap of GaAs is 1.4 eV. Calculate the optimum wavelength of light for photovoltaic generation in a GaAs solar cell​

Answer 1

Answer:

The wavelength is $\lambda = 886\ nm$

Explanation:

From the question we are told that

   The energy band gap is  $E = 1.4 eV$

Generally the wavelength is mathematically evaluated as

        $\lambda = \frac{hc}{E}$

Where h is  the Plank constant with a value $h = 4.1357 * 10{-15}$

          c is the speed of light  with constant value of $c = 3. 0 *10^{8} \ m/s$

substituting values

      $\lambda = \frac{ 4.1357 *10^{-15} * 3.0*10^{8}}{1.4}$

     $\lambda = 886\ nm$

Answer 2

The optimum wavelength of light for photovoltaic generation in a GaAs solar cell​ is equal to 886 nanometer.

Given the following data:

• Energy band gap of GaAs = 1.4 eV.

Scientific data:

• Speed of light = $3 \times 10^8\;meters$

• Planck constant = $6.626 \times 10^{-34}\;J.s$

• Charge of proton = $1.602 \times 10^{-19}\;C$

To calculate the optimum wavelength of light for photovoltaic generation in a GaAs solar cell​:

Mathematically, Einstein's equation for photon energy is given by this formula:

$E = hf = \frac{hc}{\lambda}$

Where:

• E is the energy.

• h is Plank's constant.

• $\lambda$ is the wavelength.

• c is the speed of light.

Making $\lambda$ the subject of formula, we have:

$\lambda = \frac{hc}{E}$

Substituting the given parameters into the formula, we have;

$\lambda = \frac{6.626 \times 10^{-34}\times 3 \times 10^8}{1.4 \times 1.602 \times 10^{-19}}\\\\\lambda =\frac{1.99 \times 10^{-25}}{2.2428 \times 10^{-19}} \\\\\lambda = 8.86 \times 10^{-7}\;m$

Note: $1 \;nanometer = 1 \times 10^{-9} \;meter$

Wavelength = 886 nanometer

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