Calculate the energy of the 21 cm line.
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![**Calculate the energy of the 21 cm line.**
This statement prompts users to perform a calculation involving the energy associated with electromagnetic radiation that has a wavelength of 21 centimeters.
### Detailed Explanation:
The 21 cm line refers to the electromagnetic radiation emitted or absorbed by a neutral hydrogen atom when the spin of the electron flips relative to the proton. This specific wavelength falls in the radio wave part of the electromagnetic spectrum and is an important marker in radio astronomy.
To calculate the energy ($E$) of this wavelength, you can use the formula:
\[ E = \frac{hc}{\lambda} \]
Where:
- \( E \) is the energy
- \( h \) is Planck's constant (\(6.626 \times 10^{-34} \, \text{J} \cdot \text{s}\))
- \( c \) is the speed of light (\(3.0 \times 10^8 \, \text{m/s}\))
- \( \lambda \) is the wavelength in meters (21 cm = 0.21 meters)
By substituting the values into the equation, students can solve for the energy of the 21 cm line.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fadbb6fa3-6b43-4484-8eb2-c92bfed12f92%2Fc5260deb-c28c-4fc3-b177-f731ea524457%2Fngfmk58_processed.png&w=3840&q=75)
Transcribed Image Text:**Calculate the energy of the 21 cm line.**
This statement prompts users to perform a calculation involving the energy associated with electromagnetic radiation that has a wavelength of 21 centimeters.
### Detailed Explanation:
The 21 cm line refers to the electromagnetic radiation emitted or absorbed by a neutral hydrogen atom when the spin of the electron flips relative to the proton. This specific wavelength falls in the radio wave part of the electromagnetic spectrum and is an important marker in radio astronomy.
To calculate the energy ($E$) of this wavelength, you can use the formula:
\[ E = \frac{hc}{\lambda} \]
Where:
- \( E \) is the energy
- \( h \) is Planck's constant (\(6.626 \times 10^{-34} \, \text{J} \cdot \text{s}\))
- \( c \) is the speed of light (\(3.0 \times 10^8 \, \text{m/s}\))
- \( \lambda \) is the wavelength in meters (21 cm = 0.21 meters)
By substituting the values into the equation, students can solve for the energy of the 21 cm line.
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