Multiple Choice
Given that the energy of a mole of photons is 2.83 × 10^7 J, what is the wavelength in nanometers of the light? (Use h = 6.626 × 10^{-34} J·s, c = 3.00 × 10^8 m/s, and Avogadro's number = 6.022 × 10^{23} mol^{-1})
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9. Quantum Mechanics
Wavelength and Frequency
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Given that the energy of a single photon is 2.23 × 10^{-21} J, what is the frequency of the light? (Planck's constant h = 6.626 × 10^{-34} J·s)
A
6.73 × 10^{14} Hz
B
1.49 × 10^{13} Hz
C
2.23 × 10^{-21} Hz
D
3.37 × 10^{12} Hz
Verified step by step guidance1
Recall the relationship between the energy of a photon (E) and its frequency (f), which is given by Planck's equation: \(E = h \times f\), where \(h\) is Planck's constant.
Rearrange the equation to solve for frequency: \(f = \frac{E}{h}\).
Substitute the given values into the equation: \(E = 2.23 \times 10^{-21}\) J and \(h = 6.626 \times 10^{-34}\) J·s.
Perform the division to find the frequency: \(f = \frac{2.23 \times 10^{-21}}{6.626 \times 10^{-34}}\) Hz.
Express the result in scientific notation to match the format of the answer choices.
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