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Space Physics - The Big Bang Theory and Redshift

Grade 11IGCSEPhysics

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Redshift is the increase in the observed wavelength of light emitted from distant galaxies as they move away from the Earth.

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The Doppler Effect explains that if a light source moves away from an observer, the spectral lines shift toward the red end of the spectrum (longer wavelengths, λ\lambda).

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Hubble's Law states that the recession velocity (vv) of a galaxy is directly proportional to its distance (dd) from Earth.

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The Big Bang Theory suggests that the Universe began as a very small, extremely hot, and dense region (a singularity) approximately 13.813.8 billion years ago and has been expanding ever since.

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Cosmic Microwave Background Radiation (CMBR) is the thermal radiation left over from the 'Big Bang' and provides strong evidence for the theory as it is detected uniformly from all directions in space.

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The further away a galaxy is, the faster it is moving away, which is evidenced by a greater degree of redshift.

📐Formulae

Δλλ0=λobs−λemitλemit≈vc\frac{\Delta \lambda}{\lambda_{0}} = \frac{\lambda_{obs} - \lambda_{emit}}{\lambda_{emit}} \approx \frac{v}{c}

v=H0dv = H_{0} d

Δλ=λobs−λemit\Delta \lambda = \lambda_{obs} - \lambda_{emit}

💡Examples

Problem 1:

A specific absorption line in the spectrum of a distant galaxy is measured at a wavelength of 670.4 nm670.4 \text{ nm}. The same line in a laboratory on Earth is measured at 656.3 nm656.3 \text{ nm}. Calculate the speed at which the galaxy is moving away from Earth, given the speed of light c=3.0×108 m/sc = 3.0 \times 10^8 \text{ m/s}.

Solution:

  1. Calculate the change in wavelength: Δλ=670.4 nm−656.3 nm=14.1 nm\Delta \lambda = 670.4 \text{ nm} - 656.3 \text{ nm} = 14.1 \text{ nm}.
  2. Use the redshift formula: Δλλemit=vc\frac{\Delta \lambda}{\lambda_{emit}} = \frac{v}{c}.
  3. Rearrange for velocity: v=c×Δλλemitv = c \times \frac{\Delta \lambda}{\lambda_{emit}}.
  4. Substitute values: v=(3.0×108 m/s)×14.1 nm656.3 nmv = (3.0 \times 10^8 \text{ m/s}) \times \frac{14.1 \text{ nm}}{656.3 \text{ nm}}.
  5. v≈6.45×106 m/sv \approx 6.45 \times 10^6 \text{ m/s}.

Explanation:

The change in wavelength is compared to the original emitted wavelength to find the redshift ratio. Multiplying this ratio by the speed of light provides the recession velocity of the galaxy.

Problem 2:

Explain how the observation of redshift in distant galaxies supports the Big Bang Theory.

Solution:

Redshift shows that galaxies are moving away from us. Since the light from almost all distant galaxies is redshifted, it indicates the Universe is expanding. If we extrapolate this expansion backward in time, it suggests that all matter and space originated from a single, dense point (the Big Bang).

Explanation:

Scientific theories require evidence; redshift is a primary piece of evidence for an expanding universe, which is a core tenet of the Big Bang model.

The Big Bang Theory and Redshift - Revision Notes & Key Formulas | IGCSE Grade 11 Physics