What is the energy, in joules, of a single photon with a wavelength of 400.0 nm?

• A. 4.97 \times 10^{-19} \text{ J}
• B. 7.45 \times 10^{-18} \text{ J}
• C. 2.48 \times 10^{-20} \text{ J}
• D. 3.10 \times 10^{-19} \text{ J}

Answer: (A)

Verified step by step guidance

1. Identify the formula that relates the energy of a photon to its wavelength: \(E = \frac{hc}{\lambda}\), where \(E\) is the energy of the photon, \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength.
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 \(c = 3.00 \times 10^{8} \text{ m/s}\).
3. Convert the given wavelength from nanometers to meters because SI units must be consistent: \$400.0 \text{ nm} = 400.0 \times 10^{-9} \text{ m}$.
4. Substitute the values of \(h\), \(c\), and \(\lambda\) into the formula \(E = \frac{hc}{\lambda}\) to set up the calculation for the energy of the photon.
5. Perform the division and multiplication carefully to find the energy \(E\) in joules, which will give the energy of a single photon with the given wavelength.