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(a)(i) A galaxy moves away from the Earth at a speed of 3.9 × 104 km/s.

The speed of light is 3.0 × 105 km/s.
Light from the galaxy is emitted with a wavelength of 6.2 × 10−7 m.
Calculate the change in the wavelength of the light that is received by an observer on the Earth.
(ii) Calculate the wavelength of the light that is received by the observer on the Earth.
(b)One of the pieces of evidence for the Big Bang theory is the red-shift of galaxies. Explain how the red-shift of galaxies supports the Big Bang theory.

User Walter A
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2 Answers

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(a)(i) To calculate the change in wavelength of light received by an observer on the Earth, we can use the formula for redshift:

z = ∆λ/λ = v/c

where z is the redshift, ∆λ is the change in wavelength, λ is the original wavelength, v is the velocity of the galaxy, and c is the speed of light.

Substituting the given values, we get:

z = ∆λ/6.2 × 10−7 m = 3.9 × 104 km/s / 3.0 × 105 km/s

Solving for ∆λ, we get:

∆λ = λz = 6.2 × 10−7 m × 3.9 × 104 km/s / 3.0 × 105 km/s

∆λ = 8.06 × 10−11 m

Therefore, the change in the wavelength of the light received by an observer on Earth is 8.06 × 10−11 m.

(ii) The wavelength of the light that is received by the observer on Earth can be calculated using the formula:

λ' = λ + ∆λ

where λ' is the new wavelength and λ is the original wavelength.

Substituting the given values, we get:

λ' = 6.2 × 10−7 m + 8.06 × 10−11 m

λ' = 6.2008 × 10−7 m

Therefore, the wavelength of the light received by the observer on Earth is 6.2008 × 10−7 m.

(b) The redshift of galaxies supports the Big Bang theory in two ways:

1. According to the Big Bang theory, the universe is expanding. As the universe expands, galaxies move away from each other, and their light is redshifted. The greater the redshift, the faster the galaxy is moving away from us. The observation of redshift in distant galaxies provides evidence that the universe is indeed expanding.

2. The Big Bang theory predicts that the early universe was much denser and hotter than it is now. This high density and temperature would have caused the universe to emit a lot of radiation, including light. As the universe expanded, this radiation would have cooled and stretched, leading to a cosmic microwave background radiation that fills the universe. The observed spectrum of this radiation is consistent with the predictions of the Big Bang theory. The redshift of distant galaxies provides further evidence for the Big Bang theory, as it is consistent with the idea that the universe was much denser and hotter in the past.

User Jfd
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6 votes
(a)(i) Using the formula for the Doppler effect, we can calculate the change in the wavelength of the light:
Δλ/λ = v/c
where Δλ is the change in wavelength, λ is the original wavelength, v is the speed of the galaxy, and c is the speed of light.

Substituting the values given, we get:
Δλ/6.2 × 10^-7 = 3.9 × 10^4 / 3.0 × 10^5
Δλ = 8.06 × 10^-8 m

(ii) To find the wavelength of the light received by the observer on Earth, we simply subtract the change in wavelength from the original wavelength:
λ' = λ - Δλ
λ' = 6.2 × 10^-7 - 8.06 × 10^-8
λ' = 5.39 × 10^-7 m

(b) The red-shift of galaxies supports the Big Bang theory because it provides evidence that the universe is expanding. The Doppler effect causes light from objects that are moving away from us to be shifted to longer wavelengths (i.e. red-shifted), while light from objects that are moving towards us is shifted to shorter wavelengths (i.e. blue-shifted). The observation that most galaxies are red-shifted indicates that they are moving away from us, and the degree of red-shift is proportional to the distance of the galaxy from us. This means that the farther away a galaxy is, the faster it is moving away from us. This observation supports the idea that the universe is expanding, and that it began with a Big Bang.
User Kyaw Siesein
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7.7k points
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