What is the energy (in joules) of a photon of red light with a wavelength of 675 nm? (Use h = 6.626 × 10^{-34} J·s and c = 3.00 × 10^8 m/s.)

• A. 1.47 × 10^{-19} J
• B. 2.94 × 10^{-19} J
• C. 4.41 × 10^{-19} J
• D. 6.63 × 10^{-34} J

Answer: (B)

Verified step by step guidance

1. Identify the given values: wavelength \( \lambda = 675 \text{ nm} \), Planck's constant \( h = 6.626 \times 10^{-34} \text{ J} \cdot \text{s} \), and speed of light \( c = 3.00 \times 10^{8} \text{ m/s} \).
2. Convert the wavelength from nanometers to meters because SI units must be consistent: \( 675 \text{ nm} = 675 \times 10^{-9} \text{ m} \).
3. Use the formula that relates the energy of a photon to its wavelength: \[ E = \frac{h \times c}{\lambda} \] where \( E \) is the energy, \( h \) is Planck's constant, \( c \) is the speed of light, and \( \lambda \) is the wavelength.
4. Substitute the known values into the formula: \[ E = \frac{6.626 \times 10^{-34} \times 3.00 \times 10^{8}}{675 \times 10^{-9}} \].
5. Perform the calculation carefully, keeping track of powers of ten and units, to find the energy \( E \) in joules.