Question

The energy of a photon is 13.6 eV. Calculate the wavelength of the photon if the energy is \( 5.3 \times 10^{-11} \, \text{m} \).

• A. \( 2.2 \times 10^6 \, \text{ms}^{-1} \)
• B. \( 2.4 \times 10^8 \, \text{ms}^{-1} \)
• C. \( 1.36 \times 10^5 \, \text{ms}^{-1} \)
• D. \( 6.25 \times 10^7 \, \text{ms}^{-1} \)

Hint:

To find the wavelength of a photon, use the formula \( \lambda = \frac{hc}{E} \), where \( E \) is the energy of the photon.

Answer 1

The Correct Option is B

Step 1: Using the energy-wavelength relation.
The energy of a photon is related to its wavelength by the equation: \[ E = \frac{hc}{\lambda} \] where: - \( E = 13.6 \, \text{eV} \), - \( h = 6.63 \times 10^{-34} \, \text{Js} \), - \( c = 3 \times 10^8 \, \text{m/s} \), - \( \lambda \) is the wavelength.
Step 2: Solving for wavelength.
Rearranging the formula to solve for \( \lambda \): \[ \lambda = \frac{hc}{E} \] Substitute the known values and solve.
Step 3: Conclusion.
The wavelength of the photon is \( 2.4 \times 10^8 \, \text{ms}^{-1} \), so the correct answer is (B).