Question

Determine the energy of a photon in eV if its wavelength is \( 4000\ \text{\AA} \).

• A. \( 3.1 \, \text{eV} \)
• B. \( 2.5 \, \text{eV} \)
• C. \( 1.55 \, \text{eV} \)
• D. \( 4.2 \, \text{eV} \)

Hint:

Remember the shortcut: \( E(\text{eV}) = \frac{12400}{\lambda(\text{\AA})} \) for quick calculations in photon energy problems.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The goal is to convert the wavelength of light (given in Angstroms) into the energy carried by a single photon (expressed in electron-volts).
Step 2: Key Formula or Approach:
Use the simplified energy-wavelength relation:
\[ E(eV) = \frac{12400}{\lambda(\text{\AA})} \]
This is derived from \( E = \frac{hc}{\lambda} \).
Step 3: Detailed Explanation:
Given wavelength \( \lambda = 4000\ \text{\AA} \).
Substituting into the formula:
\[ E = \frac{12400}{4000} \]
\[ E = \frac{124}{40} = 3.1 \, \text{eV} \]
Step 4: Final Answer:
The energy of the photon is \( 3.1 \, \text{eV} \).