24-10 Calculate the frequency in hertz and the energy in joules of an X-ray photon with a wavelength of 2.70stackrel (circ )(A) 4-11 . Calculate the wavelength and the energy in joules associated with a signal at 220 MHz.

To calculate the frequency in hertz and the energy in joules of an X-ray photon with a wavelength of 2.70 Å, we can use the following formulas:<br /><br />Frequency (f) = Speed of light (c) / Wavelength (λ)<br />Energy (E) = Planck's constant (h) * Frequency (f)<br /><br />Given:<br />Wavelength (λ) = 2.70 Å = 2.70 x 10^-8 m<br />Speed of light (c) = 3.00 x 10^8 m/s<br />Planck's constant (h) = 6.626 x 10^-34 J·s<br /><br />Frequency (f) = c / λ<br />Frequency (f) = (3.00 x 10^8 m/s) / (2.70 x 10^-8 m)<br />Frequency (f) = 1.11 x 10^17 Hz<br /><br />Energy (E) = h * f<br />Energy (E) = (6.626 x 10^-34 J·s) * (1.11 x 10^17 Hz)<br />Energy (E) = 7.35 x 10^-17 J<br /><br />Therefore, the frequency of the X-ray photon is 1.11 x 10^17 Hz, and the energy is 7.35 x 10^-17 J.<br /><br />To calculate the wavelength and the energy associated with a signal at 220 MHz, we can use the following formulas:<br /><br />Wavelength (λ) = Speed of light (c) / Frequency (f)<br />Energy (E) = Planck's constant (h) * Frequency (f)<br /><br />Given:<br />Frequency (f) = 220 MHz = 220 x 10^6 Hz<br />Speed of light (c) = 3.00 x 10^8 m/s<br />Planck's constant (h) = 6.626 x 10^-34 J·s<br /><br />Wavelength (λ) = c / f<br />Wavelength (λ) = (3.00 x 10^8 m/s) / (220 x 10^6 Hz)<br />Wavelength (λ) = 1.36 x 10^-2 m = 13.6 μm<br /><br />Energy (E) = h * f<br />Energy (E) = (6.626 x 10^-34 J·s) * (220 x 10^6 Hz)<br />Energy (E) = 1.46 x 10^-26 J<br /><br />Therefore, the wavelength associated with the signal at 220 MHz is 13.6 μm, and the energy is 1.46 x 10^-26 J.