What is the energy of an electromagnetic wave that has a frequency of $8.0 \times 10^{15} Hz$ ? Use the equation $E=h f$, where $h=6.626 \times 10^{-34} J \cdot s$.
A. $1.2 \times 10^{49} J$
B. $1.2 \times 10^{-49} J$
C. $5.3 \times 10^{18} J$
D. $5.3 \times 10^{-18} J
Answer (2)
Substitute the given values into the equation: E = h f .
Calculate the energy: E = ( 6.626 × 1 0 − 34 J ⋅ s ) × ( 8.0 × 1 0 15 Hz ) .
The result of the calculation is E = 5.3008 × 1 0 − 18 J .
The energy of the electromagnetic wave is 5.3 × 1 0 − 18 J .
Explanation
Understanding the Problem We are given the frequency of an electromagnetic wave, f = 8.0 \t × 1 0 15 Hz , and Planck's constant, h = 6.626 \t × 1 0 − 34 J \t ⋅ s . We need to find the energy E of the electromagnetic wave using the equation E = h f .
Setting up the Calculation To find the energy E , we will substitute the given values of h and f into the equation E = h f .
Calculating the Energy Now, we perform the calculation: E = ( 6.626 \t × 1 0 − 34 J \t ⋅ s ) \t × ( 8.0 \t × 1 0 15 Hz ) E = 5.3008 \t × 1 0 − 18 J
Determining the Answer Comparing the calculated value with the given options, we find that the energy of the electromagnetic wave is approximately 5.3 \t × 1 0 − 18 J . Therefore, the correct answer is D.
Examples
Electromagnetic waves, like the ones used in your microwave or X-ray machines, carry energy. This problem demonstrates how to calculate the energy of a single electromagnetic wave (photon) given its frequency. Knowing the energy of electromagnetic waves is crucial in various applications, such as designing medical imaging devices, understanding the effects of radiation, and developing efficient communication technologies. For instance, if you know the frequency of the X-rays used in a medical scan, you can calculate the energy delivered to the patient's body.
The energy of an electromagnetic wave with a frequency of 8.0 × 1 0 15 Hz is calculated using Planck's equation as 5.3 × 1 0 − 18 J . The correct answer from the provided options is D. This calculation demonstrates how frequency can be used to determine the energy of electromagnetic radiation.
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