An 800 nm spectral line when observed from a galaxy is shifted to 920 nm. Calculate the redshift.
An 800 nm spectral line when observed from a galaxy is shifted to 920 nm. Calculate the redshift.
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![### Redshift Calculation
**Problem Statement:**
An 800 nm spectral line when observed from a galaxy is shifted to 920 nm. Calculate the redshift.
**Explanation:**
Redshift is a key concept in understanding the universe's expansion. It occurs when light or other electromagnetic radiation from an object is increased in wavelength, or shifted to the red end of the spectrum. This phenomenon is typically expressed as the dimensionless number, "z," calculated using the formula:
\[ z = \frac{\lambda_{\text{observed}} - \lambda_{\text{emitted}}}{\lambda_{\text{emitted}}} \]
**Given Data:**
- \( \lambda_{\text{emitted}} = 800 \, \text{nm} \)
- \( \lambda_{\text{observed}} = 920 \, \text{nm} \)
**Calculation:**
\[ z = \frac{920 \, \text{nm} - 800 \, \text{nm}}{800 \, \text{nm}} = \frac{120 \, \text{nm}}{800 \, \text{nm}} = 0.15 \]
Therefore, the redshift \( z \) is 0.15.
**Conclusion:**
The calculated redshift indicates how fast the galaxy is moving away from us, suggesting that it is part of the expanding universe.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18a542a1-0899-4ebe-acd6-685d74e53e0e%2F1d359cc7-954a-4ab5-9f1b-e43caec7f7e6%2Fkdfdz23_processed.png&w=3840&q=75)
Transcribed Image Text:### Redshift Calculation
**Problem Statement:**
An 800 nm spectral line when observed from a galaxy is shifted to 920 nm. Calculate the redshift.
**Explanation:**
Redshift is a key concept in understanding the universe's expansion. It occurs when light or other electromagnetic radiation from an object is increased in wavelength, or shifted to the red end of the spectrum. This phenomenon is typically expressed as the dimensionless number, "z," calculated using the formula:
\[ z = \frac{\lambda_{\text{observed}} - \lambda_{\text{emitted}}}{\lambda_{\text{emitted}}} \]
**Given Data:**
- \( \lambda_{\text{emitted}} = 800 \, \text{nm} \)
- \( \lambda_{\text{observed}} = 920 \, \text{nm} \)
**Calculation:**
\[ z = \frac{920 \, \text{nm} - 800 \, \text{nm}}{800 \, \text{nm}} = \frac{120 \, \text{nm}}{800 \, \text{nm}} = 0.15 \]
Therefore, the redshift \( z \) is 0.15.
**Conclusion:**
The calculated redshift indicates how fast the galaxy is moving away from us, suggesting that it is part of the expanding universe.
Expert Solution
Concept and Principle:
- Redshift is the process by which light from moving sources is shifted to longer wavelengths.
- Redshift is calculated using,
Here lobs is the observed wavelength and lrest is the actual wavelength.
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