Ch.13 - Solids & Modern Materials

Problem 71

Chapter 13, Problem 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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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.

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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Conversion Factors

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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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Key Concepts

Photon Energy

Band Gap Energy

Energy Conversion

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)?