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Answer: a
Explanation: The band gap energy in electron volt when wavelength is given is, Eg =
1.24(μm)/λ = 1.24 x 10-6/1240 x 10-9 = 1eV.
The band gap energy of a material can be determined when light of a certain wavelength is incident on it using the equation:
[ E = frac{hc}{lambda} ]
where:
– (E) is the band gap energy in electron volts (eV),
– (h) is Planck’s constant ((6.626 times 10^{-34}) m(^2)kg/s),
– (c) is the speed of light in vacuum ((3.00 times 10^8) m/s),
– (lambda) is the wavelength of the incident light in meters.
Given:
– Wavelength (lambda = 1240) nm = (1240 times 10^{-9}) m (since (1) nm = (10^{-9}) m)
First, convert constants and given values to compatible units (if necessary, but they are already compatible in our case), and then use the equation to find (E).
[ E = frac{(6.626 times 10^{-34}, text{m}^2text{kg/s})(3.00 times 10^8, text{m/s})}{1240 times 10^{-9}, text{m}} ]
[ E = frac{1.9878 times 10^{-25}, text{m}^2text{kg/s}}{124