Question

A photon has an energy of \( 3.2 \times 10^{-19} \, \text{J} \). What is the frequency of the photon?

• A. \( 5.0 \times 10^{14} \, \text{Hz} \)
• B. \( 4.0 \times 10^{14} \, \text{Hz} \)
• C. \( 3.0 \times 10^{14} \, \text{Hz} \)
• D. \( 6.0 \times 10^{14} \, \text{Hz} \)

Hint:

Remember: The energy of a photon is directly proportional to its frequency. The higher the frequency, the greater the energy of the photon.

Answer 1

The Correct Option is A

We are given the energy of the photon:

\( E = 3.2 \times 10^{-19} \, \text{J} \)

We use the formula for photon energy:

\[ E = h \cdot f \]

Where:

• \( E \) is the energy of the photon,
• \( h = 6.626 \times 10^{-34} \, \text{J} \cdot \text{s} \) is Planck's constant,
• \( f \) is the frequency of the photon.

Step 1: Rearranging the formula to solve for frequency:

\[ f = \frac{E}{h} \]

Step 2: Substituting the values:

\[ f = \frac{3.2 \times 10^{-19}}{6.626 \times 10^{-34}} = 4.83 \times 10^{14} \, \text{Hz} \]

Conclusion:

The frequency of the photon is approximately Option 1: \( 5.0 \times 10^{14} \, \text{Hz} \).