Question

cumulative exam
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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:

To solve this, we use the relationship between energy (\(E\)), frequency (\(f\)), and wavelength (\(\lambda\)) of electromagnetic waves: \(E = hf\) (where \(h\) is Planck's constant) and \(c = f\lambda\) (where \(c\) is the speed of light). So, energy is directly proportional to frequency (\(E \propto f\)) and inversely proportional to wavelength (\(E \propto \frac{1}{\lambda}\)) because \(f=\frac{c}{\lambda}\), so \(E = \frac{hc}{\lambda}\).

• Analyze Option 1: Gamma rays have shorter wavelengths than microwaves. Since \(E \propto \frac{1}{\lambda}\), shorter wavelength means higher energy. So gamma rays (shorter \(\lambda\)) have higher energy than microwaves. This matches the energy - wavelength relationship.
• Analyze Option 2: Gamma rays have higher frequency (not lower) than microwaves (since \(E \propto f\) and gamma rays have higher energy). So this is incorrect.
• Analyze Option 3: Infrared light has longer (not shorter) wavelengths than X - rays. Since \(E \propto \frac{1}{\lambda}\), longer wavelength means lower energy, but the reason about wavelength is wrong here.
• Analyze Option 4: Infrared light has lower frequency (not higher) than X - rays (since \(E \propto f\) and X - rays have higher energy). So this is incorrect.

Answer:

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