A beam of light is shined on a thin (sub-millimeter thick) single crystal wafer of material. The light source is special since it can be tun

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A beam of light is shined on a thin (sub-millimeter thick) single crystal wafer of material. The light source is special since it can be tuned to provide any wavelength of visible light on demand. The specimen is illuminated such that the wavelength of light is increased over time while the transmitted intensity of the light is measured. If the sample becomes transparent when the wavelength is greater than 690 nanometers, what is the band gap of the material, in eV

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  1. Answer:

    The energy gap of the material is [tex]E_G = 1.7982 eV[/tex]

    Explanation:

    From the question we are told that

        The wavelength is [tex]\lambda = 690 nm[/tex]

    The band gap of the material can be mathematically represented as

                   [tex]E_G = \frac{h c}{\lambda }[/tex]

    Where h is the Planck constant with value  [tex]h = 6.626 *10^{-34} joule \cdot sec[/tex]

               c is the speed of light with a value [tex]c = 3.0*10^8[/tex]

        Substituting value

                  [tex]E_G =\frac{6.626 *10^{-34} 3 *10^{8}}{690 *10^{-9}}[/tex]

                       [tex]= 2.8809 *10^{-19}J[/tex]

    Now converting to eV we divide by the charge on on electron. the value is  

            [tex]e = 1.602 *10^{-19 } C[/tex]

         so

             [tex]E_G = \frac{2..8809 *10^{-19}}{1.602 *10^{-19}}[/tex]

             [tex]E_G = 1.7982 eV[/tex]

                 

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