What is the energy of a single photon of light that has a frequency of 2.30 × 10^{17} Hz? (Use Planck's constant h = 6.626 × 10^{-34} J·s.)

• A. 3.48 × 10^{-17} J
• B. 6.626 × 10^{-34} J
• C. 9.89 × 10^{-15} J
• D. 1.52 × 10^{-16} J

Answer: (D)

Verified step by step guidance

1. Recall the formula that relates the energy of a photon to its frequency: \(E = h \times \nu\), where \(E\) is the energy of the photon, \(h\) is Planck's constant, and \(\nu\) (nu) is the frequency of the light.
2. Identify the given values from the problem: frequency \(\nu = 2.30 \times 10^{17}\) Hz and Planck's constant \(h = 6.626 \times 10^{-34}\) J·s.
3. Substitute the given values into the formula: \(E = (6.626 \times 10^{-34}) \times (2.30 \times 10^{17})\).
4. Multiply the numerical coefficients (6.626 and 2.30) and add the exponents of 10 according to the rules of exponents when multiplying powers of ten.
5. Express the final answer in proper scientific notation to represent the energy of a single photon in joules.