n. Estimate the relative velocity.
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![**Problem Statement:**
A 0.75 m radio signal is detected from a galaxy as 2.0 m. Estimate the relative velocity.
**Explanation:**
This problem involves the concept of redshift, which occurs when the wavelength of light or other electromagnetic radiation from an object is increased (shifted to the red end of the spectrum). This is commonly seen with galaxies receding from us due to the expansion of the universe.
**Calculations:**
To estimate the relative velocity (v), we use the formula related to redshift (\(z\)):
\[ z = \frac{\lambda_{\text{observed}} - \lambda_{\text{emitted}}}{\lambda_{\text{emitted}}} \]
Where:
- \(\lambda_{\text{observed}}\) is the observed wavelength (2.0 m).
- \(\lambda_{\text{emitted}}\) is the emitted wavelength (0.75 m).
First, calculate the redshift:
\[ z = \frac{2.0 \, \text{m} - 0.75 \, \text{m}}{0.75 \, \text{m}} = \frac{1.25 \, \text{m}}{0.75 \, \text{m}} \approx 1.67 \]
For velocities much less than the speed of light, we can use the approximation:
\[ v = z \times c \]
Where \(c\) is the speed of light (\(3 \times 10^8 \, \text{m/s}\)).
Thus, the relative velocity is:
\[ v \approx 1.67 \times 3 \times 10^8 \, \text{m/s} \approx 5.01 \times 10^8 \, \text{m/s} \]
This result shows that the galaxy is receding at a significant fraction of the speed of light, indicating the expansion of the universe's effect.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F440b7269-170b-4024-8d0e-4b8a2f594bf7%2F4c3512d0-18d9-4e88-9f28-eb557579d512%2Fhqy08_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A 0.75 m radio signal is detected from a galaxy as 2.0 m. Estimate the relative velocity.
**Explanation:**
This problem involves the concept of redshift, which occurs when the wavelength of light or other electromagnetic radiation from an object is increased (shifted to the red end of the spectrum). This is commonly seen with galaxies receding from us due to the expansion of the universe.
**Calculations:**
To estimate the relative velocity (v), we use the formula related to redshift (\(z\)):
\[ z = \frac{\lambda_{\text{observed}} - \lambda_{\text{emitted}}}{\lambda_{\text{emitted}}} \]
Where:
- \(\lambda_{\text{observed}}\) is the observed wavelength (2.0 m).
- \(\lambda_{\text{emitted}}\) is the emitted wavelength (0.75 m).
First, calculate the redshift:
\[ z = \frac{2.0 \, \text{m} - 0.75 \, \text{m}}{0.75 \, \text{m}} = \frac{1.25 \, \text{m}}{0.75 \, \text{m}} \approx 1.67 \]
For velocities much less than the speed of light, we can use the approximation:
\[ v = z \times c \]
Where \(c\) is the speed of light (\(3 \times 10^8 \, \text{m/s}\)).
Thus, the relative velocity is:
\[ v \approx 1.67 \times 3 \times 10^8 \, \text{m/s} \approx 5.01 \times 10^8 \, \text{m/s} \]
This result shows that the galaxy is receding at a significant fraction of the speed of light, indicating the expansion of the universe's effect.
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