Question

A photon has an energy of \( 5.0 \, \text{eV} \). What is its wavelength? (Planck's constant \( h = 6.626 \times 10^{-34} \, \text{J} \cdot \text{s} \), speed of light \( c = 3.0 \times 10^8 \, \text{m/s} \))

• A. \( 400 \, \text{nm} \)
• B. \( 500 \, \text{nm} \)
• C. \( 600 \, \text{nm} \)
• D. \( 700 \, \text{nm} \)

Hint:

The energy of a photon is inversely proportional to its wavelength. Use \( E = \frac{h c}{\lambda} \) to calculate the wavelength when the energy is known.

Answer 1

The Correct Option is A

The energy of a photon is related to its wavelength \( \lambda \) by the equation: \[ E = \frac{h c}{\lambda} \] Where: - \( E = 5.0 \, \text{eV} \) (energy of the photon), - \( h = 6.626 \times 10^{-34} \, \text{J} \cdot \text{s} \) (Planck's constant), - \( c = 3.0 \times 10^8 \, \text{m/s} \) (speed of light), - \( \lambda \) is the wavelength. First, convert the energy from electron volts to joules: \[ E = 5.0 \, \text{eV} \times 1.602 \times 10^{-19} \, \text{J/eV} = 8.01 \times 10^{-19} \, \text{J} \] Now solve for \( \lambda \): \[ \lambda = \frac{h c}{E} \] Substitute the known values: \[ \lambda = \frac{6.626 \times 10^{-34} \times 3.0 \times 10^8}{8.01 \times 10^{-19}} \] \[ \lambda = 2.48 \times 10^{-9} \, \text{m} = 400 \, \text{nm} \] Thus, the wavelength of the photon is \( 400 \, \text{nm} \).