Finding the speed of quaser using the Doppler equation

In summary, the Hβ line of the hydrogen atom's spectrum has a normal wavelength of 486 nm. When observed in the spectrum of a distant quasar, the same line is lengthened by 19.0 nm. Using the equation f' = f(1 - u/c), where f' is the observed frequency, f is the normal frequency, u is the speed of the quasar, and c is the speed of light, we can solve for the speed of the quasar relative to Earth. The calculated speed is 1.17e7 m/s, which is correct.
  • #1
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Homework Statement


The Hβ line of the hydrogen atom's spectrum has a normal wavelength λβ= 486 nm. This same line is observed in the spectrum of a distant quasar, but lengthened by 19.0nm . What is the speed of the quasar relative to Earth, assuming it is moving along our line of sight?


Homework Equations



f' = f(1 + u/c)

The Attempt at a Solution



I converted the wavelengths into frequencies to solve for u and got 6.17e14 Hz = 5.94e14 Hz(1+ u/3e8m/s)). Then I solve for u and keep getting 1.17e7 m/s, which is incorrect. What am I doing wrong?
 
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  • #2
You should have 486 nm and 505 nm for the two frequencies. The frequency equation should be f' = f(1 - u/c) if the quasar is moving away from us. Solving for u you will get 1.17e7 m/s which is the correct answer.
 

Related to Finding the speed of quaser using the Doppler equation

1. How do you measure the speed of a quasar using the Doppler equation?

The Doppler equation is used to measure the speed of an object by analyzing the frequency of its emitted light. For quasars, astronomers look for a shift in the spectral lines of the emitted light, known as the redshift or blueshift, which can be used to calculate the speed of the quasar.

2. Can the Doppler equation accurately measure the speed of all types of quasars?

The Doppler equation can accurately measure the speed of quasars as long as they are emitting light and have a measurable redshift or blueshift. However, there are some types of quasars that do not have a strong enough emission to accurately measure their speed using the Doppler equation.

3. What factors can affect the accuracy of using the Doppler equation to measure the speed of a quasar?

The accuracy of the Doppler equation depends on the precision of the instruments used to measure the redshift or blueshift of the quasar's emitted light. Other factors that can affect the accuracy include the distance of the quasar from Earth and any external forces, such as gravitational interactions, that may be affecting its speed.

4. How can knowing the speed of a quasar help scientists understand the universe?

Knowing the speed of a quasar can provide valuable information about the expansion of the universe and the distance between celestial objects. It can also help scientists better understand the formation and evolution of galaxies and the role of supermassive black holes in the universe.

5. Is the Doppler equation the only method used to measure the speed of quasars?

The Doppler equation is one of the most commonly used methods to measure the speed of quasars, but it is not the only one. Other methods, such as gravitational lensing and the use of standard candles, can also be used to determine the speed of quasars and other celestial objects in the universe.

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