What is the frequency of a photon with an energy of 4.56 $10^{-19} J$?
A. $6.42 x 10^{14} Hz$
B. $5.10 x 10^{14} Hz$
C. $6.88 x 10^{14} Hz$
D. $4.36 x 10^{14} Hz
Answer (2)
The frequency of a photon with an energy of 4.56 × 1 0 − 19 J is calculated to be approximately 6.88 × 1 0 14 Hz , making the correct choice C . This is determined using the relationship between energy and frequency through Planck's constant.
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The problem provides the energy of a photon and asks for its frequency.
Use the formula E = h f to relate energy and frequency, where h is Planck's constant.
Rearrange the formula to solve for frequency: f = h E .
Substitute the given values and calculate: f = 6.626 × 1 0 − 34 4.56 × 1 0 − 19 ≈ 6.88 × 1 0 14 Hz . The final answer is 6.88 × 1 0 14 Hz .
Explanation
Understanding the Problem We are given the energy of a photon and asked to find its frequency. We know that the energy of a photon is related to its frequency by the equation E = h f , where E is the energy, h is Planck's constant, and f is the frequency.
Identify Given Values We are given:
Energy, E = 4.56 \t \t × 1 0 − 19 J
Planck's constant, h = 6.626 \t \t × 1 0 − 34 J s
We need to find the frequency, f .
Rearrange the Formula We can rearrange the formula E = h f to solve for the frequency f :
f = h E
Substitute the Values Now, we substitute the given values into the formula:
f = 6.626 \t \t × 1 0 − 34 J s 4.56 \t \t × 1 0 − 19 J
Calculate the Frequency Calculating the frequency:
f = 6.626 \t \t × 1 0 − 34 4.56 \t \t × 1 0 − 19 ≈ 6.88 \t \t × 1 0 14 Hz
Final Answer The frequency of the photon is approximately 6.88 \t \t × 1 0 14 Hz . Therefore, the correct answer is C.
Examples
Understanding the frequency of photons is crucial in various real-world applications. For example, in medical imaging, different frequencies of electromagnetic radiation, such as X-rays, are used to visualize bones and tissues. In telecommunications, specific frequencies of radio waves are used to transmit information wirelessly. Moreover, in solar energy, the frequency of sunlight determines the efficiency of solar panels in converting light into electricity. By understanding the relationship between energy and frequency, we can better harness and utilize electromagnetic radiation for various technological advancements.
