You observe a spectral line of hydrogen at a wavelength of \(502.3 \mathrm{nm}\) in a distant galaxy. The rest wavelength of this line is \(486.1 \mathrm{nm} .\) What is the radial velocity of this galaxy? Is it moving toward you or away from you?

In astronomy, redshift occurs when the wavelength of light from a celestial object stretches out and shifts to the red end of the spectrum. This happens when an object moves away from the observer. Redshift is a key concept when studying the expanding universe and distant galaxies.

To identify redshift, you compare the observed wavelength of light with the rest wavelength—the latter being the wavelength if the light source were stationary relative to the observer. If the observed wavelength is longer, it's redshifted, indicating the object is moving away.

• This effect is due to the Doppler effect.
• Redshift can tell us about the speed and direction of galaxies.
• It helps in measuring the rate of expansion of the universe.

In the given exercise, the hydrogen spectral line's observed wavelength is 502.3 nm, while the rest wavelength is 486.1 nm. Since the observed wavelength is greater, the galaxy is redshifted. This means it's moving away from us.

Radial velocity refers to the speed at which an object moves toward or away from an observer. It is measured along the line of sight. In astronomy, it’s crucial for understanding the motions of stars and galaxies.

The radial velocity is calculated using the Doppler shift formula:

### Doppler Shift Formula
The formula is:
dist rest\rad observed\rad c (speed of light), approximately 3 × 10^8 m/s.

• If the observed wavelength is greater than the rest wavelength, the object moves away, and velocity is positive.
• If it’s smaller, the object moves toward the observer, and velocity is negative.

In the exercise, substituting the observed (502.3 nm) and rest (486.1 nm) wavelengths into the formula, the radial velocity 'v' is:
v = \(\boxed v = 3 \times 10^8 \frac{\boxed{502.3 m - 486.1 m}}{\boxed{486.1 m}} \boxed \frac{\boxed{16.2m}}{\boxed{486.1m}}.\boxed}This results in \)1.00 \times \boxed{$10^7. This positive result confirms the galaxy is moving away from us.

Spectral lines are specific wavelengths of light that are either absorbed or emitted by elements and molecules in a star or galaxy’s atmosphere. Each element has a unique pattern of lines, acting like a fingerprint.

These lines help astronomers identify the chemical composition and physical conditions of celestial objects. Spectral lines can also reveal the velocity of an object through the Doppler effect.

• Emission lines show wavelengths where light is emitted.
• Absorption lines show wavelengths where light is absorbed.
• The position of these lines can shift due to motion, indicating velocity.

In our exercise, the hydrogen spectral line observed at 502.3 nm compared to its rest wavelength of 486.1 nm helps us determine the galaxy's radial velocity. Since the line is redshifted, we know the galaxy is moving away from us.