How much energy does an individual photon of 470 nm light possess?

• A. 2.65 imes 10^{-19} J
• B. 8.45 imes 10^{-20} J
• C. 4.23 imes 10^{-19} J
• D. 1.41 imes 10^{-18} J

Answer: (C)

Verified step by step guidance

1. Identify the formula to calculate the energy of a single photon, which is given by \(E = \frac{hc}{\lambda}\), where \(E\) is the energy of the photon, \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength of the light.
2. Write down the known constants: Planck's constant \(h = 6.626 \times 10^{-34} \text{ J}\cdot\text{s}\), and the speed of light \(c = 3.00 \times 10^{8} \text{ m/s}\). Also, convert the wavelength from nanometers to meters: \$470 \text{ nm} = 470 \times 10^{-9} \text{ m}$.
3. Substitute the values into the formula: \(E = \frac{(6.626 \times 10^{-34})(3.00 \times 10^{8})}{470 \times 10^{-9}}\).
4. Perform the division and multiplication carefully to find the energy \(E\) in joules, keeping track of the powers of ten.
5. Compare the calculated energy value with the given options to identify the correct energy possessed by a photon of 470 nm light.