Chapter 1: Problem 3
Consider a photon at \(1 \mathrm{THz}\). (a) What is the energy of the photon in terms of electron-volts? (b) What is the energy of the photon in joules? (c) Is this more or less than the random kinetic energy of an electron at room temperature \((300 \mathrm{~K}) ?\) (d) Discuss if it is necessary to consider quantum effects of the 1 THz photon at room temperature.
Short Answer
Step by step solution
Convert THz to Hz
Calculate Energy in joules
Convert Joules to Electron-volts
Compare with Average Kinetic Energy
Convert Kinetic Energy to Electron-volts
Compare Energies and Discuss Quantum Effects
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
THz to Hz conversion
Energy of photon in joules
\[ E = (6.62607015 \times 10^{-34}) \times (1 \times 10^{12}) = 6.62607015 \times 10^{-22} \text{ J} \]
This tells us how much energy this particular photon carries in joules.
Energy of photon in electron-volts
\[ E_{\text{eV}} = \frac{6.62607015 \times 10^{-22}}{1.602176634 \times 10^{-19}} \approx 4.14 \times 10^{-3} \text{ eV} \]
This value tells us that the photon's energy is quite small when expressed in electron-volts.
Kinetic energy at room temperature
\[ E_{\text{kin}} = \frac{3}{2} (1.380649 \times 10^{-23}) (300) \approx 6.21 \times 10^{-21} \text{ J} \]
Converting this kinetic energy to eV, we get:
\[ E_{\text{kin,eV}} = \frac{6.21 \times 10^{-21}}{1.602176634 \times 10^{-19}} \approx 0.0388 \text{ eV} \]
The kinetic energy of an electron at room temperature is significantly higher than the energy of a 1 THz photon.
Quantum effects
In summary, low-energy photons, such as those at 1 THz, are often overshadowed by thermal energy at common temperatures, reducing the noticeable impact of quantum effects in such scenarios.