Question

The frequency of a photon of energy 1.326 eV is:

• A. \(1.18 \times 10^{14} \, \text{Hz}\)
• B. \(3.20 \times 10^{14} \, \text{Hz}\)
• C. \(4.20 \times 10^{15} \, \text{Hz}\)
• D. \(4.80 \times 10^{15} \, \text{Hz}\)

Hint:

To find the frequency of a photon, use \( f = \frac{E}{h} \), where \( E \) is in eV and \( h = 4.1357 \times 10^{-15} \, \text{eV·s} \). This avoids unit conversion if energy is given in eV.

Answer 1

The Correct Option is B

Step 1: Use the relationship between energy and frequency of a photon.
The energy \( E \) of a photon is related to its frequency \( f \) by: \[ E = h f \] \[ f = \frac{E}{h} \] where \( h \) is Planck’s constant (\( h = 4.1357 \times 10^{-15} \, \text{eV·s} \)). Step 2: Convert the given energy.
The energy of the photon is given as: \[ E = 1.326 \, \text{eV} \] Step 3: Calculate the frequency.
Using \( h = 4.1357 \times 10^{-15} \, \text{eV·s} \): \[ f = \frac{E}{h} = \frac{1.326}{4.1357 \times 10^{-15}}} \approx 3.206 \times 10^{14} \, \text{Hz} \] Step 4: Match with the options.
The calculated frequency \( 3.206 \times 10^{14} \, \text{Hz} \) is closest to option (B) \( 3.20 \times 10^{14} \, \text{Hz} \).