Calculating Frequency of Hydrogen Light in a Moving Galaxy

[_Mayday_]

Homework Statement

A galaxy is moving away from the Earth at a speed of [tex]2.3\times 10^7 m/s^1[/tex]. Hydrogen emits light of wavelength 410nm. The speed of light is [tex]3.0\times 10^8 m/s^1[/tex] Calculate th frequency of hydrogen light emission that you would expect to measure on earth.

Homework Equations

I'm not really sure! I would have thought judging by what I have done previous to this.

[tex]V=f\lambda[/tex]

[tex] \frac{\Delta f}{f} = \frac {v}{c}[/tex]

The Attempt at a Solution

I really can't think of anything, I would have thought there were 2 steps to it. Possibly the first equation to find the frequency of Hygrogen? I'm really stuck

Help would be great

 

[psi^]

All you have to do is to compute the change in frequency due to Doppler's Effect, you have the speed of the source and the speed of the wave.
Check the general section on the wiki for more details on the formulas :)
http://en.wikipedia.org/wiki/Doppler_effect

 

[Moetasim]

I would approach this problem by first recognizing that the observed wavelength of the hydrogen light will be affected by the motion of the galaxy. This is known as the Doppler effect, and it causes a shift in the wavelength of light emitted from a moving source. In this case, the galaxy is moving away from Earth, so the observed wavelength will be longer (redshifted).

To calculate the frequency of the hydrogen light on Earth, we can use the equation V = fλ, where V is the velocity, f is the frequency, and λ is the wavelength. We know the velocity of the galaxy (V) and the wavelength of the hydrogen light on Earth (λ = 410nm). Plugging these values into the equation, we can solve for the frequency (f).

f = V/λ = (2.3x10^7 m/s)/(410x10^-9 m) = 5.6x10^13 Hz

This is the frequency of the hydrogen light that we would expect to measure on Earth. However, since the galaxy is moving away from us, the light will be redshifted and the observed frequency will be slightly lower. To account for this, we can use the equation Δf/f = v/c, where Δf is the change in frequency, v is the velocity, and c is the speed of light. Plugging in our values, we get:

Δf/f = (2.3x10^7 m/s)/(3.0x10^8 m/s) = 0.077

This means that the observed frequency will be 0.077 times lower than the calculated frequency. Therefore, the final frequency of the hydrogen light that we would expect to measure on Earth is:

f = 0.077 x 5.6x10^13 Hz = 4.3x10^12 Hz

In conclusion, as a scientist, I would approach this problem by using the Doppler effect to account for the motion of the galaxy and then using the equations V = fλ and Δf/f = v/c to calculate the frequency of the hydrogen light that we would expect to measure on Earth. This approach can be applied to similar problems involving the motion of astronomical objects and the measurement of light from them.