Questions: Some of the light that atomic hydrogen can emit has wavelengths of 21 cm (radio), 656 nm (red), 1.88 µm (infrared), 410 nm (violet), and 122 nm (ultraviolet). Arrange these from fastest speed to slowest speed in empty space. cm=10^-2 m (centimeters), µm=10^-6 m (microns), and nm=10^-9 m (nanometers).
There is not enough information to determine the speeds.
122 nm, 410 nm, 656 nm, 1.88 µm, 21 cm
21 cm, 1.88 µm, 656 nm, 410 nm, 122 nm
1.88 µm, 21 cm, 122 nm, 410 nm, 656 nm
They all travel at the same speed.
Transcript text: Some of the light that atomic hydrogen can emit has wavelengths of 21 cm (radio), 656 nm (red), $1.88 \mu \mathrm{~m}$ (infrared), 410 nm (violet), and 122 nm (ultraviolet). Arrange these from fastest speed to slowest speed in empty space. $\mathrm{cm}=10^{-2} \mathrm{~m}$ (centimeters), $\mu \mathrm{m}=10^{-6} \mathrm{~m}$ (microns), and $\mathrm{nm}=10^{-9} \mathrm{~m}$ (nanometers).
There is not enough information to determine the speeds.
$122 \mathrm{~nm}, 410 \mathrm{~nm}, 656 \mathrm{~nm}, 1.88 \mu \mathrm{~m}, 21 \mathrm{~cm}$
$21 \mathrm{~cm}, 1.88 \mu \mathrm{~m}, 656 \mathrm{~nm}, 410 \mathrm{~nm}, 122 \mathrm{~nm}$
$1.88 \mu \mathrm{~m}, 21 \mathrm{~cm}, 122 \mathrm{~nm}, 410 \mathrm{~nm}, 656 \mathrm{~nm}$
They all travel at the same speed.
Solution
Solution Steps
Step 1: Understanding the Speed of Light in Empty Space
In empty space, all electromagnetic waves, regardless of their wavelength, travel at the same speed, which is the speed of light, \( c \approx 3.00 \times 10^8 \) m/s.
Step 2: Analyzing the Given Wavelengths
The given wavelengths are:
21 cm (radio)
656 nm (red)
\(1.88 \, \mu \mathrm{m}\) (infrared)
410 nm (violet)
122 nm (ultraviolet)
Step 3: Determining the Speed of Light for Each Wavelength
Since all electromagnetic waves travel at the same speed in empty space, the speed of light for each of these wavelengths is the same.
Final Answer
\(\boxed{\text{They all travel at the same speed.}}\)