What is the energy, in joules, of a UV photon with a wavelength of 254 nm?

• A. 7.83 × 10^{-19} J
• B. 2.45 × 10^{-17} J
• C. 1.25 × 10^{-18} J
• D. 4.90 × 10^{-19} J

Answer: (A)

Verified step by step guidance

1. Identify the formula to calculate the energy of a photon, which is given by \(E = \frac{hc}{\lambda}\), where \(E\) is the energy, \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength of the photon.
2. Write down the known constants: Planck's constant \(h = 6.626 \times 10^{-34}\) J·s, and the speed of light \(c = 3.00 \times 10^{8}\) m/s.
3. Convert the wavelength from nanometers to meters because SI units must be consistent. Since \$1\( nm = \)1 \times 10^{-9}\( m, calculate \)\lambda = 254 \times 10^{-9}$ m.
4. Substitute the values of \(h\), \(c\), and \(\lambda\) into the formula \(E = \frac{hc}{\lambda}\) to set up the calculation for the photon's energy.
5. Perform the division and multiplication carefully to find the energy \(E\) in joules, ensuring the units cancel properly to give energy in joules (J).