Question

the model of the electromagnetic spectrum shows the different types of electromagnetic waves and their respective wavelengths and frequencies. the electromagnetic spectrum select the true statements. x - rays and infrared waves travel at the speed of light. a radio wave carries more energy than an ultraviolet wave. the shorter the wavelength of an electromagnetic wave, the greater the energy it carnes. the frequency and energy of an electromagnetic wave are related by the speed of light, c

Explanation:

• X - rays and infrared waves travel at the speed of light: All electromagnetic waves (including X - rays and infrared) travel at the speed of light (\(c = 3\times10^{8}\space m/s\)) in a vacuum.
• A radio wave carries more energy than an ultraviolet wave: Energy of an electromagnetic wave is given by \(E = h

u=\frac{hc}{\lambda}\), where \(h\) is Planck's constant, \(
u\) is frequency and \(\lambda\) is wavelength. Radio waves have longer wavelengths (lower frequencies) than ultraviolet waves. So, radio waves have less energy than ultraviolet waves.

• The shorter the wavelength of an electromagnetic wave, the greater the energy it carries: From \(E=\frac{hc}{\lambda}\), as \(\lambda\) (wavelength) decreases, \(E\) (energy) increases.
• The frequency and energy of an electromagnetic wave are related by the speed of light, \(c\): \(E = h

u\) (direct relationship between energy \(E\) and frequency \(
u\)), and \(c=\lambda
u\). But the fundamental relationship for energy and frequency is \(E = h
u\) (not directly using \(c\) in the energy - frequency relationship formula in the most basic sense. The energy - frequency relationship is a direct Planck's law relationship \(E = h
u\)).

Answer:

• X - rays and infrared waves travel at the speed of light.
• The shorter the wavelength of an electromagnetic wave, the greater the energy it carries.