Which of the following frequencies of light has the highest energy?

• A. 1.0 \times 10^{15} \text{ Hz}
• B. 2.0 \times 10^{14} \text{ Hz}
• C. 5.0 \times 10^{14} \text{ Hz}
• D. 8.0 \times 10^{13} \text{ Hz}

Answer: (A)

Verified step by step guidance

1. Recall the relationship between the energy of a photon and its frequency, which is given by the equation \(E = h \times f\), where \(E\) is the energy, \(h\) is Planck's constant, and \(f\) is the frequency of the light.
2. Understand that Planck's constant \(h\) is a fixed value (\$6.626 \times 10^{-34}$ J·s), so the energy of a photon is directly proportional to its frequency.
3. Compare the given frequencies: \$1.0 \times 10^{15}\( Hz, \)2.0 \times 10^{14}\( Hz, \)5.0 \times 10^{14}\( Hz, and \)8.0 \times 10^{13}$ Hz.
4. Since energy increases with frequency, identify the highest frequency among the options, which corresponds to the highest energy.
5. Conclude that the frequency \$1.0 \times 10^{15}$ Hz has the highest energy because it is the largest frequency value given.