Q: A spectral line of wavelength 6000 Å from a star is observed to be shifted towards the red by 5 Å. The speed of recession of the star is (c = 3 × 10⁸ m/s):

2.5 \times 10^{5} m/s. v = c(Δλ/λ) = (3 × 10⁸)(5/6000) = 3 × 10⁸ × 8.33 × 10⁻⁴ = 2.5 × 10⁵ m/s.

Question 1

The Doppler effect in light is the apparent change in the _____ of light due to relative motion between the source and the observer.

Accepted Answer

Frequency (and wavelength). Relative motion between source and observer changes the observed frequency and wavelength of light — the Doppler effect.

Question 2

When a light source moves away from an observer, the observed wavelength:

Accepted Answer

Increases (red shift). A receding source produces a red shift — the observed wavelength increases (frequency decreases).

Question 3

A blue shift in the spectrum of a star indicates that the star is:

Accepted Answer

Approaching the observer. A blue shift (decrease in wavelength) means the source is approaching, so light is shifted towards higher frequency.

Question 4

For a source moving with radial speed v much smaller than c, the fractional change in wavelength is given approximately by:

Accepted Answer

\dfrac{\Delta\lambda}{\lambda} = \dfrac{v}{c}. For v ≪ c, the Doppler shift is Δλ/λ ≈ v/c (with v the radial component of velocity).

Question 5

Unlike the Doppler effect for sound, the Doppler effect for light depends only on:

Accepted Answer

The relative velocity of source and observer. Light needs no medium, so only the relative velocity between source and observer matters (there is no separate "medium" frame as with sound).

Question 6

The radial speed of a receding star can be found from its red shift using:

Accepted Answer

v = c\,\dfrac{\Delta\lambda}{\lambda}. From Δλ/λ = v/c, the radial speed is v = c(Δλ/λ).

Question 7

A spectral line of wavelength 6000 Å from a star is observed to be shifted towards the red by 5 Å. The speed of recession of the star is (c = 3 × 10⁸ m/s):

Accepted Answer

2.5 	imes 10^{5} m/s. v = c(Δλ/λ) = (3 × 10⁸)(5/6000) = 3 × 10⁸ × 8.33 × 10⁻⁴ = 2.5 × 10⁵ m/s.

Question 8

The observation that the spectral lines of distant galaxies are red-shifted led to the conclusion that:

Accepted Answer

The universe is expanding. The systematic red shift of distant galaxies (Hubble's observation) indicates they are receding — evidence that the universe is expanding.

Question 9

One edge (limb) of the rotating Sun shows a slight blue shift while the opposite edge shows a red shift. This is because:

Accepted Answer

One edge approaches while the other recedes due to the Sun's rotation. As the Sun rotates, one limb moves towards us (blue shift) and the other moves away (red shift), allowing its rotational speed to be measured.

Question 10

A galaxy is receding at 3 × 10⁶ m/s. The fractional red shift Δλ/λ of its spectral lines is:

Accepted Answer

0.01. Δλ/λ = v/c = (3 × 10⁶)/(3 × 10⁸) = 0.01 (a 1% red shift).

Question 11

A spectral line of 5000 Å from a star shifts by +2.5 Å towards the red. The recession speed is (c = 3 × 10⁸ m/s):

Accepted Answer

1.5 × 10⁵ m/s. v = c(Δλ/λ) = 3 × 10⁸ × 2.5/5000 = 1.5 × 10⁵ m/s.

Question 12

A galaxy recedes at 6 × 10⁶ m/s. Its fractional red shift Δλ/λ is (c = 3 × 10⁸ m/s):

Accepted Answer

0.02. Δλ/λ = v/c = 6 × 10⁶/3 × 10⁸ = 0.02.

Question 13

A 6000 Å line is observed at 6006 Å from a receding source. The speed of recession is (c = 3 × 10⁸ m/s):

Accepted Answer

3 × 10⁵ m/s. Δλ = 6 Å; v = c(6/6000) = 3 × 10⁵ m/s.

Question 14

A star approaches at 1.5 × 10⁶ m/s. The fractional blue shift of a spectral line is (c = 3 × 10⁸ m/s):

Accepted Answer

0.005. Δλ/λ = v/c = 1.5 × 10⁶/3 × 10⁸ = 0.005 (towards shorter wavelength).

Question 15

A 4000 Å line from a galaxy is red-shifted to 4004 Å. The recession speed is (c = 3 × 10⁸ m/s):

Accepted Answer

3 × 10⁵ m/s. Δλ = 4 Å; v = c(4/4000) = 3 × 10⁵ m/s.

Question 16

For a source receding at 3 × 10⁷ m/s, the shift of a 5000 Å line is (c = 3 × 10⁸ m/s):

Accepted Answer

500 Å (red). Δλ = λ(v/c) = 5000 × (3 × 10⁷/3 × 10⁸) = 5000 × 0.1 = 500 Å.

Doppler Effect in Light — MH-CET Physics MCQs with Solutions

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