In observing an oxygen emission line from a warm gas cloud that is expected to appear at 500 nm, the line is seen at 525 nm instead (5% longer). Which of the following is true?
A. The observed emission line indicates that a chemical change has occurred.
B. The object is moving toward the observer at 5% of the speed of light.
C. The object is moving away from the observer at 5% of the speed of light.
D. The observer's equipment is inaccurate since emission lines do not change.
E. The velocity of the light is greater than expected.
Answer (1)
Calculate the redshift using the formula: z = expected wavelength observed wavelength − expected wavelength = 0.05 .
Relate the redshift to the velocity using the formula: v = z × c .
Determine that the object is moving away from the observer at 5% of the speed of light.
The correct answer is C.
Explanation
Understanding the Problem We are given that an oxygen emission line expected at 500 nm is observed at 525 nm. This indicates a redshift, meaning the wavelength is longer than expected. We need to determine the correct statement about this observation.
Calculating Redshift First, let's calculate the redshift (z). The formula for redshift is: z = expected wavelength observed wavelength − expected wavelength Plugging in the given values: z = 500 nm 525 nm − 500 nm = 500 nm 25 nm = 0.05
Relating Redshift to Velocity The redshift (z) is related to the velocity (v) of the object relative to the observer by the formula: z = c v where c is the speed of light. Therefore, the velocity is: v = z × c = 0.05 × c This means the object is moving away from the observer at 5% of the speed of light.
Analyzing the Options Now, let's analyze the given options: OA. The observed emission line indicates that a chemical change has occurred. - This is incorrect because redshift is related to motion, not chemical changes. OB. The object is moving toward the observer at 5% of the speed of light. - This is incorrect because a redshift indicates the object is moving away from the observer. OC. The object is moving away from the observer at 5% of the speed of light. - This is the correct answer. OD. The observer's equipment is inaccurate since emission lines do not change. - This is incorrect because emission lines do change due to the Doppler effect. E. The velocity of the light is greater than expected. - This is incorrect because the speed of light is constant.
Conclusion Therefore, the correct answer is that the object is moving away from the observer at 5% of the speed of light.
Examples
Imagine you are observing a distant galaxy. The light from that galaxy is emitted at specific wavelengths. If the galaxy is moving away from us, the wavelengths of the light will be stretched, appearing 'redder' than they should be. By measuring this redshift, we can determine how fast the galaxy is moving away from us. This is similar to how the pitch of a siren changes as an ambulance moves past you; the sound waves are stretched (lower pitch) as the ambulance moves away.
