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: Establish the photon energy-frequency relationship. The energy \( E \) of a photon is defined by its frequency \( f \) via the equation: \[E = h f\] which can be rearranged to: \[f = \frac{E}{h}\] Here, \( h \) represents Planck’s constant, with a value of \( h = 4.1357 \times 10^{-15} \, \text{eV·s} \).Step 2: Input the given photon energy. The energy is provided as: \[E = 1.326 \, \text{eV}\]Step 3: Compute the frequency. Using the value of \( h = 4.1357 \times 10^{-15} \, \text{eV·s} \): \[f = \frac{E}{h} = \frac{1.326}{4.1357 \times 10^{-15}}} \approx 3.206 \times 10^{14} \, \text{Hz}\]Step 4: Select the matching option. The computed frequency, \( 3.206 \times 10^{14} \, \text{Hz} \), is nearest to option (B) \( 3.20 \times 10^{14} \, \text{Hz} \).