What is the energy of a photon that emits a light of frequency $7.21 \times 10^{14} Hz$?
A. $4.78 x 10^{-19} J$
B. $2.76 x 10^{-19} J$
C. $1.09 \times 10^{-19} J$
D. $4.16 x 10^{-19} J
Answer (2)
The energy of a photon emitted at a frequency of 7.21 × 1 0 14 Hz can be calculated using the formula E = h f . This calculation yields an energy of approximately 4.78 × 1 0 − 19 J , which corresponds to option A. Therefore, the correct answer is 4.78 × 1 0 − 19 J .
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Use the formula E = h f to calculate the energy of a photon.
Substitute the given frequency f = 7.21 \tims 1 0 14 Hz and Planck's constant h = 6.626 \tims 1 0 − 34 J s into the formula.
Calculate the energy: E = ( 6.626 \tims 1 0 − 34 J s ) \tims ( 7.21 \tims 1 0 14 Hz ) = 4.78 \tims 1 0 − 19 J .
The energy of the photon is 4.78 × 1 0 − 19 J .
Explanation
Understanding the Problem We are given the frequency of light emitted by a photon and asked to find the energy of the photon. We know that the energy of a photon can be calculated using the formula E = h f , where E is the energy, h is Planck's constant, and f is the frequency. Planck's constant is approximately 6.626 \tims 1 0 − 34 J s .
Applying the Formula We are given the frequency f = 7.21 \tims 1 0 14 Hz . We can now substitute the values of h and f into the formula: E = ( 6.626 \tims 1 0 − 34 J s ) \tims ( 7.21 \tims 1 0 14 Hz )
Calculating the Energy Now, we perform the calculation: E = 6.626 \tims 7.21 \tims 1 0 − 34 + 14 J E = 47.77346 \tims 1 0 − 20 J E = 4.777346 \tims 1 0 − 19 J Rounding to two decimal places, we get E = 4.78 \tims 1 0 − 19 J .
Final Answer Comparing our result with the given options, we see that option A, 4.78 \tims 1 0 − 19 J , matches our calculated energy. Therefore, the energy of the photon is 4.78 \tims 1 0 − 19 J .
Examples
Understanding the energy of photons is crucial in various fields. For example, in solar panels, photons from sunlight strike the panel and transfer their energy to electrons, generating electricity. The efficiency of this process depends on the energy of the photons, which is directly related to their frequency. Similarly, in medical imaging techniques like PET scans, the energy of emitted photons is used to create detailed images of the body's internal structures. The relationship between energy and frequency is also fundamental in understanding the colors we see, as different frequencies of light correspond to different colors.
