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

The photon's energy is provided as:

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

The relationship between photon energy and frequency is given by:

\[ E = h \cdot f \]

Where:

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

Step 1: The formula is rearranged to isolate frequency:

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

Step 2: Values are substituted into the rearranged formula:

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

Conclusion:

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