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. radio waves and ultraviolet waves travel at the same speed in a vacuum. a high - frequency electromagnetic wave carries a greater amount of energy than a low - frequency electromagnetic wave. the longer the wavelength of an electromagnetic wave, the greater the energy it carries. the energy of one quantum depends on the frequency of the electromagnetic wave.

Explanation:

• All electromagnetic waves (including radio and ultraviolet waves) travel at the speed of light (\(c = 3\times10^{8}\ m/s\)) in a vacuum. So, the statement "Radio waves and ultraviolet waves travel at the same speed in a vacuum" is true.
• The energy of an electromagnetic wave is given by \(E=h

u\), where \(h\) is Planck's constant (\(h = 6.626\times 10^{-34}\ J\cdot s\)) and \(
u\) is the frequency. Since \(h>0\), a higher - frequency (\(
u\)) wave has more energy. So, the statement "A high - frequency electromagnetic wave carries a greater amount of energy than a low - frequency electromagnetic wave" is true.

• The energy of an electromagnetic wave is \(E = h

u=\frac{hc}{\lambda}\) (where \(\lambda\) is the wavelength). As \(\lambda\) increases, \(E\) decreases (because \(h\) and \(c\) are constants). So, the statement "The longer the wavelength of an electromagnetic wave, the greater the energy it carries" is false.

• The energy of one quantum (photon) of an electromagnetic wave is \(E = h

u\), which depends on the frequency \(
u\) of the wave. So, the statement "The energy of one quantum depends on the frequency of the electromagnetic wave" is true.

Answer:

• Radio waves and ultraviolet waves travel at the same speed in a vacuum.
• A high - frequency electromagnetic wave carries a greater amount of energy than a low - frequency electromagnetic wave.
• The energy of one quantum depends on the frequency of the electromagnetic wave.