What is the energy of a photon with a frequency of [tex]$2.2 \times 10^{16} Hz$[/tex]? Planck's constant is [tex]$6.63 \times 10^{-34} J \cdot s$[/tex].
A. [tex]$1.5 \times 10^{-17} J$[/tex]
B. [tex]$8.8 \times 10^{-17} J$[/tex]
C. [tex]$1.5 \times 10^{-16} J$[/tex]
D. [tex]$8.8 \times 10^{-16} J$[/tex]
Answer (2)
Use the formula E = h f to find the energy of a photon.
Substitute the given values: h = 6.63 × 1 0 − 34 J ⋅ s and f = 2.2 × 1 0 16 Hz .
Calculate the energy: E = ( 6.63 × 1 0 − 34 ) × ( 2.2 × 1 0 16 ) = 1.4586 × 1 0 − 17 J .
The energy of the photon is approximately 1.5 × 1 0 − 17 J .
Explanation
Understanding the Problem We are given the frequency of a photon and Planck's constant, and we need to find the energy of the photon. The formula that relates energy, frequency, and Planck's constant is E = h f , where E is the energy, h is Planck's constant, and f is the frequency.
Identifying Given Values We are given: Frequency, f = 2.2 × 1 0 16 Hz Planck's constant, h = 6.63 × 1 0 − 34 J ⋅ s We need to find the energy E .
Calculating the Energy Using the formula E = h f , we substitute the given values: E = ( 6.63 × 1 0 − 34 J ⋅ s ) × ( 2.2 × 1 0 16 Hz ) E = 1.4586 × 1 0 − 17 J The result of the operation is 1.4586 × 1 0 − 17 J .
Final Answer The energy of the photon is approximately 1.4586 × 1 0 − 17 J . Among the given options, the closest value is 1.5 × 1 0 − 17 J .
Examples
Understanding the energy of photons is crucial in various fields. For example, in medical imaging, X-rays, which are high-energy photons, are used to create images of bones and tissues. The energy of these photons determines their ability to penetrate different materials, allowing doctors to diagnose various conditions. Similarly, in solar panels, photons from sunlight are absorbed by semiconductor materials, generating electricity. The efficiency of solar panels depends on their ability to capture and convert the energy of these photons into electrical energy. This principle is also applied in understanding the radiation emitted by stars and other celestial objects, helping astronomers determine their composition and distance.
The energy of a photon with a frequency of 2.2 × 1 0 16 Hz is calculated using Planck's equation, resulting in approximately 1.5 × 1 0 − 17 J . Therefore, the correct answer is option A.
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