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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 at each of the frequencies listed in problem 1.

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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