The fact that the speed of light is constant as it travels through a vacuum means that
a. X-rays can be transmitted through the atmosphere around the world.
b. radio wave photons have shorter wavelengths than gamma-ray photons.
c. all photons have the same wavelength.
d. photons with longer wavelengths have lower frequencies.
e. ultraviolet photons have less energy than visible photons.
The correct answer and explanation is:
The correct answer is d. photons with longer wavelengths have lower frequencies.
Explanation:
The speed of light in a vacuum is constant, approximately 3 x 10^8 meters per second. This fact is fundamental to the nature of electromagnetic waves, including light. The speed of light is related to the frequency and wavelength of the electromagnetic wave by the equation: c=λ⋅fc = \lambda \cdot f
Where:
- c is the speed of light in a vacuum,
- λ (lambda) is the wavelength of the wave, and
- f is the frequency of the wave.
Since the speed of light is constant, the wavelength and frequency are inversely related. This means that if the wavelength of a photon increases, its frequency must decrease to maintain the constant speed of light. Therefore, photons with longer wavelengths indeed have lower frequencies.
Let’s look at the other options:
- a. X-rays can be transmitted through the atmosphere around the world: This is incorrect. X-rays are largely absorbed by the Earth’s atmosphere and do not travel easily through it.
- b. Radio wave photons have shorter wavelengths than gamma-ray photons: This is incorrect. Radio waves have much longer wavelengths compared to gamma rays.
- c. All photons have the same wavelength: This is incorrect. Photons can have different wavelengths, depending on the type of electromagnetic radiation they represent, such as radio waves, visible light, and gamma rays.
- e. Ultraviolet photons have less energy than visible photons: This is incorrect. Ultraviolet photons have higher energy than visible photons because their wavelengths are shorter.
Thus, the inverse relationship between wavelength and frequency, as dictated by the constant speed of light, is best described by option d.