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Ch.13 - Solids & Modern Materials
Tro - Chemistry: A Molecular Approach 6th Edition
Tro6th EditionChemistry: A Molecular ApproachISBN: 9780137832217Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoTro 6th EditionCh.13 - Solids & Modern MaterialsProblema 71
Capitolo 13, Problema 71

Does a photon of red light with a frequency of 4.29⨉1014 Hz have sufficient energy to promote an electron from the valence band to the conduction band in a sample of silicon (the band gap in silicon is 1.11 eV)?

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Identify the energy of the photon using the formula: \( E = h \cdot f \), where \( h \) is Planck's constant \( 6.626 \times 10^{-34} \text{ J} \cdot \text{s} \) and \( f \) is the frequency of the photon.
Convert the energy from joules to electronvolts (eV) using the conversion factor: \( 1 \text{ eV} = 1.602 \times 10^{-19} \text{ J} \).
Compare the energy of the photon in eV to the band gap energy of silicon, which is 1.11 eV.
Determine if the photon's energy is greater than or equal to the band gap energy to decide if it can promote an electron from the valence band to the conduction band.
Conclude whether the photon has sufficient energy based on the comparison.

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Photon Energy

The energy of a photon is directly related to its frequency and can be calculated using the equation E = hν, where E is energy, h is Planck's constant (6.626 x 10^-34 J·s), and ν is the frequency of the light. For red light with a frequency of 4.29 x 10^14 Hz, this relationship allows us to determine if the photon has enough energy to affect electron transitions in materials.
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01:40
Photon Energy Formulas

Band Gap Energy

The band gap energy is the energy difference between the valence band and the conduction band in a semiconductor. In silicon, this band gap is approximately 1.11 eV, which means that an electron must gain at least this amount of energy to transition from the valence band to the conduction band, allowing for electrical conductivity.
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03:13
Intepreting the Band of Stability

Energy Conversion

To determine if the photon can promote an electron in silicon, we must convert the photon's energy from electron volts (eV) to joules (J) or vice versa. Since 1 eV is equivalent to 1.602 x 10^-19 J, this conversion is essential for comparing the energy of the photon with the band gap energy of silicon to see if the transition is possible.
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01:56
Conversion Factors
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