In the laboratory,a spectral line of an element has a wavelength of 5000 Angstroms.What would be the measured wavelength of that line in the spectrum of a planet that is approaching at a velocity of 30 km/s? (The speed of light is 300,000 km/s. )
A)4999.5 Angstroms
B)4995 Angstroms
C)5000.5 Angstroms
D)5005 Angstroms

Question

Quizplus · Accepted Answer

The wavelength appears shorter (blue-shifted) due to the Doppler effect, as the planet is approaching. The change in wavelength ($\Delta \lambda$) can be calculated using the formula $\Delta \lambda = \lambda \times \frac{v}{c}$, where $\lambda$ is the original wavelength, $v$ is the velocity of the object, and $c$ is the speed of light. Here, $\Delta \lambda = 5000 \times \frac{30}{300,000} = 0.5$ Angstroms. Thus, the new wavelength is $5000 - 0.5 = 4999.5$ Angstroms.

In the Laboratory,a Spectral Line of an Element Has a Wavelength