What is the energy of a single photon of light that has a frequency of 9.28 \times 10^{22} \text{ Hz}?

• A. 6.15 \times 10^{-11} \text{ J}
• B. 6.15 \times 10^{-11} \text{ J}
• C. 6.15 \times 10^{10} \text{ J}
• D. 6.15 \times 10^{-12} \text{ J}

Answer: (A)

Verified step by step guidance

1. Identify 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 \(\nu\) is the frequency of the light.
2. Recall the value of Planck's constant, which is \(h = 6.626 \times 10^{-34} \text{ J} \cdot \text{s}\).
3. Substitute the given frequency \(\nu = 9.28 \times 10^{22} \text{ Hz}\) and Planck's constant into the formula: \(E = (6.626 \times 10^{-34}) \times (9.28 \times 10^{22})\).
4. Multiply the numerical coefficients and add the exponents of 10 according to the rules of exponents: \(a \times 10^{m} \times b \times 10^{n} = (a \times b) \times 10^{m+n}\).
5. Express the final energy value in proper scientific notation and units of joules (J) to find the energy of the single photon.