Question

the energy of microwaves is less than the energy of ultraviolet light. which comparison of the energies of electromagnetic waves is correct? gamma rays have higher energy than microwaves because gamma rays have shorter wavelengths. gamma rays have higher energy than microwaves because gamma rays have lower frequencies. infrared light has lower energy than x - rays because infrared light has shorter wavelengths. infrared light has lower energy than x - rays because infrared light has higher frequencies.

Explanation:

Step1: Recall the energy - wavelength and energy - frequency relationship

The energy of an electromagnetic wave is given by \(E = h
u=\frac{hc}{\lambda}\), where \(h\) is Planck's constant, \(
u\) is the frequency, \(c\) is the speed of light, and \(\lambda\) is the wavelength. So, \(E\propto
u\) (direct proportionality between energy and frequency) and \(E\propto\frac{1}{\lambda}\) (inverse proportionality between energy and wavelength).

Step2: Analyze each option

• Option 1:

Gamma rays have shorter wavelengths than microwaves. Since \(E=\frac{hc}{\lambda}\), shorter - wavelength electromagnetic waves have higher energy. So, gamma rays (\(\lambda_{\text{gamma}}\ll\lambda_{\text{microwave}}\)) have higher energy than microwaves.

• Option 2:

Since \(E = h
u\), higher - frequency waves have higher energy. Gamma rays have higher frequencies (\(
u_{\text{gamma}}\gg
u_{\text{microwave}}\)) than microwaves, not lower frequencies. So, this option is wrong.

• Option 3:

Infrared light has longer wavelengths (\(\lambda_{\text{infrared}}>\lambda_{X - ray}\)) than X - rays. Using \(E=\frac{hc}{\lambda}\), longer - wavelength (infrared) has lower energy. But the reason given (shorter wavelengths for infrared) is wrong.

• Option 4:

Using \(E = h
u\), X - rays have higher frequencies (\(
u_{X - ray}>
u_{\text{infrared}}\)) than infrared light. The reason given (higher frequencies for infrared) is wrong.

Answer:

Gamma rays have higher energy than microwaves because gamma rays have shorter wavelengths.