Unit 5
Class 12 Physics
Chapter number not exposed on the legacy source page
Red Shift
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Introduction
When the spectral lines received from an astronomical source appear at longer wavelengths than their known rest wavelengths, the phenomenon is called red shift. A common cause is relative recession between the source and observer. In astronomy, redshift is a central observational tool for estimating motion and studying the expansion of the universe.
Red shift: Displacement of observed spectral features toward longer wavelength (the red end of the visible spectrum) compared with their rest wavelengths.
Diagram 1: Receding source and stretched wavelength
Doppler Effect for Light
The Doppler effect is the apparent change in observed frequency or wavelength due to relative motion between source and observer. For electromagnetic waves, recession leads to lower observed frequency and longer wavelength; approach leads to higher frequency and shorter wavelength.
c = fλ
Since the speed of light in vacuum c is fixed, an increase in observed wavelength corresponds to a decrease in observed frequency.
Important distinction: Astronomical redshift can arise from ordinary relative motion, cosmic expansion and gravitational effects. At Class 12 level, the essential calculation is usually based on wavelength shift and recession speed.
Red Shift and Blue Shift
| Feature | Red shift | Blue shift |
|---|---|---|
| Relative motion (simple Doppler interpretation) | Source recedes | Source approaches |
| Observed wavelength | Increases | Decreases |
| Observed frequency | Decreases | Increases |
| Spectral displacement | Toward red/long-wavelength side | Toward blue/violet/short-wavelength side |
Diagram 2: Shift of spectral lines
Redshift Parameter
Let λ0 be the rest wavelength and λobs the observed wavelength. The redshift parameter is:
z = (λobs − λ0)/λ0 = Δλ/λ0
For red shift, z > 0. For blue shift, z < 0 under this sign convention.
Diagram 3: Meaning of the redshift parameter
Common mistake: Use the rest/emitted wavelength in the denominator, not the observed wavelength.
Recession Velocity from Red Shift
For speeds much smaller than the speed of light:
z ≈ v/c
v ≈ c(Δλ/λ0)
where c ≈ 3.00×108 m s−1.
Exam important: The approximation v ≈ cz is suitable only for relatively small z/non-relativistic recession speeds. For very large redshifts, a relativistic/cosmological treatment is required.
Relativistic Doppler relation (useful extension)
For pure special-relativistic radial recession:
1 + z = √[(1+β)/(1−β)], β = v/cThis is scientifically more accurate at high speed, but use it only when the question or course level requires it.
Red Shift and Hubble’s Law
Redshifts of distant galaxies provide evidence that, on large scales, galaxies are receding as the universe expands. Hubble’s law states that recession speed is proportional to distance for nearby/low-redshift galaxies:
v = H0d
where H0 is the Hubble constant and d is distance.
Diagram 4: Hubble relation
Diagram 5: Expansion analogy
Interpretation: Redshift observations support an expanding-universe picture. They do not mean every nearby object must recede; local gravitationally bound systems can have their own motions.
Worked Numerical Examples
Example 1: Find redshift and recession speed. A spectral line has rest wavelength 500 nm and is observed at 505 nm.
Δλ = 5 nm.
z = 5/500 = 0.010 v ≈ zc = 0.010×3.00×108 = 3.0×106 m s−1So v ≈ 3000 km s−1.
Example 2: Find observed wavelength. A galaxy recedes at 1500 km s−1. A line has rest wavelength 600 nm. Find λobs using the low-speed approximation.
v/c = 1500/(3.0×105) = 0.005.
Δλ = (v/c)λ0 = 0.005×600 nm = 3 nm λobs = 603 nmExample 3: Hubble-law distance. If a galaxy has recession speed 7000 km s−1 and H0 = 70 km s−1 Mpc−1, estimate its distance.
d = v/H0 = 7000/70 = 100 Mpc
Important Concepts and Exam Notes
- Spectral lines are useful because their laboratory/rest wavelengths are known precisely.
- Red shift means λobs > λ0; blue shift means λobs < λ0.
- The fractional wavelength shift is dimensionless.
- For small speeds, Δλ/λ ≈ v/c.
- Always state the direction: recession produces red shift; approach produces blue shift in the simple Doppler picture.
- Hubble’s law links large-scale recession speed and distance and is one observational foundation of expanding-universe cosmology.
Common mistakes:
- Confusing wavelength increase with frequency increase. Because c=fλ, longer wavelength means lower frequency.
- Forgetting to use consistent units for c and v.
- Using the non-relativistic relation v=cz at very large z without qualification.
- Calling every redshift “ordinary Doppler shift”; cosmological and gravitational redshift also exist.
Important Exam Questions
Short-answer
- Define red shift and blue shift.
- What happens to wavelength and frequency when a star recedes from Earth?
- Define the redshift parameter z.
- State Hubble’s law and write the physical meaning of H0.
- Why are spectral lines useful for measuring astronomical redshift?
Long-answer / derivation
- Explain red shift using the Doppler effect and derive v ≈ cΔλ/λ for small recession speeds.
- Explain how redshift observations support the idea of an expanding universe.
- State Hubble’s law, sketch the v–d graph and explain how its slope is interpreted.
Numerical questions
- A line of rest wavelength 656.3 nm is observed at 660.0 nm. Calculate z and the approximate recession speed.
- A galaxy recedes at 4500 km s−1. Calculate the shift of a 500 nm spectral line using the low-speed relation.
- Given H0 = 70 km s−1 Mpc−1, estimate the distance of a galaxy receding at 3500 km s−1.
Diagram questions
- Draw a labelled rest spectrum and red-shifted spectrum.
- Draw a receding source with stretched wavefronts.
- Draw and label a Hubble-law graph.
One-Minute Revision
- Red shift = displacement toward longer wavelength.
- Blue shift = displacement toward shorter wavelength.
- c = fλ, so red shift corresponds to lower observed frequency.
- z = (λobs−λ₀)/λ₀.
- For small speeds: z ≈ v/c.
- Therefore v ≈ cz.
- Positive z indicates red shift under the usual convention.
- Spectral lines provide known reference wavelengths.
- Hubble law: v = H₀d.
- Large-scale galactic redshifts are key evidence for cosmic expansion.
- Use relativistic/cosmological treatment when z is not small.
Diagram Practice
- Receding star and wavelength stretching
- Rest vs red-shifted spectral lines
- Redshift formula concept
- Hubble graph
- Expansion analogy
Source handling: The original Nepal eNotes PDF is embedded above using the supplied Google Drive file. The typed section follows the verified NEB/CDC syllabus and is designed as a searchable, responsive study companion. Where the PDF viewer does not expose handwritten page text, the typed section is a syllabus-aligned reconstruction and is not claimed to be a word-for-word transcription.
Curriculum note: The legacy page treats Red Shift as a standalone note. The newer CDC Grade 12 Physics textbook discusses red/blue shift within Doppler effect in Acoustic Phenomenon, while older NEB curriculum materials also connect red shift with Hubble’s law and cosmology. This page therefore focuses tightly on red shift, its calculation and its cosmological interpretation without assigning an unverified legacy chapter number.
Curriculum note: The legacy page treats Red Shift as a standalone note. The newer CDC Grade 12 Physics textbook discusses red/blue shift within Doppler effect in Acoustic Phenomenon, while older NEB curriculum materials also connect red shift with Hubble’s law and cosmology. This page therefore focuses tightly on red shift, its calculation and its cosmological interpretation without assigning an unverified legacy chapter number.
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