Question

The wavelength of a photon is 500 nm. Calculate its energy. (Planck’s constant \( h = 6.63 \times 10^{-34} \, \text{J·s} \), speed of light \( c = 3 \times 10^8 \, \text{m/s} \))

• A. \( 3.98 \times 10^{-19} \, \text{J} \)
• B. \( 4.14 \times 10^{-19} \, \text{J} \)
• C. \( 5.24 \times 10^{-19} \, \text{J} \)
• D. \( 2.48 \times 10^{-19} \, \text{J} \)

Hint:

Use $E = \frac{hc}{\lambda}$ to calculate photon energy. Convert wavelength to meters before substitution.

Answer 1

The Correct Option is A

The energy of a photon is calculated using the formula: \[ E = \frac{hc}{\lambda} \] where \( h \) is Planck's constant, \( c \) is the speed of light, and \( \lambda \) is the wavelength. The provided values are: \[ h = 6.63 \times 10^{-34} \, \text{J} \cdot \text{s}, \quad c = 3 \times 10^8 \, \text{m/s}, \quad \lambda = 500 \, \text{nm} = 5 \times 10^{-7} \, \text{m} \] Substituting these values yields: \[ E = \frac{(6.63 \times 10^{-34}) \times (3 \times 10^8)}{5 \times 10^{-7}} = \frac{1.989 \times 10^{-25}}{5 \times 10^{-7}} \approx 3.978 \times 10^{-19} \, \text{J} \] Thus, the photon energy is approximately: \[ E \approx 3.98 \times 10^{-19} \, \text{J} \]