What is the energy, in joules, of a photon with a wavelength of 21 nm? (Use h = 6.626 × 10^{-34} J·s and c = 3.00 × 10^{8} m/s.)

• A. 3.17 × 10^{-19} J
• B. 6.33 × 10^{-17} J
• C. 1.42 × 10^{-16} J
• D. 9.47 × 10^{-18} J

Answer: (D)

Verified step by step guidance

1. Identify the given values: wavelength \( \lambda = 21 \text{ nm} \), 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 are required: \( 21 \text{ nm} = 21 \times 10^{-9} \text{ m} \).
3. Recall the formula for the energy of a photon: \[ E = \frac{h \times c}{\lambda} \] where \( E \) is 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: \[ E = \frac{6.626 \times 10^{-34} \times 3.00 \times 10^{8}}{21 \times 10^{-9}} \].
5. Perform the calculation carefully, keeping track of powers of ten, to find the energy \( E \) in joules.