Thank you for visiting Please show all work 1 Calculate the wavelength of each frequency a 100 2 MHz b 1070 kHz 2 Calculate the energy of a photon. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
We calculated the wavelength for each frequency using the speed of light equation, yielding results of 2.99 m and 280.4 m respectively. Then, using Planck's equation, we found the energy for each frequency, obtaining 6.64 * [tex]10^{-25 }[/tex]J and 7.09 *[tex]10^{-28}[/tex] J respectively.
Explanation:
The subject of these problems is Physics, specifically quantum mechanics and wave motion. In Part 1, we calculate the wavelength of different frequencies using the speed of light equation: Speed of Light (c) = Wavelength (λ) * Frequency (ν). Given that the speed of light is approximately 3.00 * [tex]10^8[/tex] meters/second, we can rearrange this equation to find the wavelength: λ = c / v. For 100.2 MHz (which is the same as 100.2 * [tex]10^6[/tex] Hz), the wavelength would be
λ = (3.00 * [tex]10^8[/tex] m/s) / (100.2 * [tex]10^6[/tex] 1/s)
= 2.99 m. Similarly, for 1070 KHz (or 1070 * [tex]10^3[/tex] Hz), λ
= (3.00 * [tex]10^8[/tex]m/s) / (1070 * 10^3 1/s) = 280.4 m.
In Part 2, we calculate the energy of the photon for each frequency using the Planck's equation: Energy (E) = Planck’s Constant (h) * Frequency (ν). Given Planck's constant is approximately 6.63 * [tex]10^{-34}[/tex] J*s, we find that for 100.2 MHz,
E = (6.63 * [tex]10^{-34 }[/tex]J*s) * (100.2 * [tex]10^6[/tex]1/s)
= 6.64 * [tex]10^{-25}[/tex] J. For 1070 KHz, E = (6.63 *[tex]10^{-34}[/tex] J*s) * (1070 * [tex]10^{3}[/tex] 1/s) = 7.09 *[tex]10^{-28 }[/tex]J. In conclusion, these calculations require a solid understanding of how wavelength, frequency, and energy are interconnected.
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