Question

We can learn a lot about the properties of a star by studying its spectrum. All of the followingstatements are true except one. Which one?A. the peak of the star’s thermal emission tells us its temperature: Hotter stars peak at shorter (blue) wavelengths.B. The total amount of light in the spectrum tells us the star’s radius.C. We can look at Doppler shifts of spectral lines to determine the star’s speed toward or away from us.D. we can identify chemical elements present in the star by recognizing patterns of spectral lines that correspond to particular chemicals

Answer 1

B. The total amount of light in the spectrum tells us the star’s radius.

Step-by-step explanation:

A.

The effective temperature of a star can be determined by means of its spectrum¹ and Wien's displacement law.

Since stars behave in a local way as a blackbody, it will take the wavelength at which is the peak of emission greater in the continuum (see the image below).

Then, the maximum peak of emission (
`\lambda_(max)`) will be replaced in the next equation of the Wien's displacement law:

`T = (2.898x10^(-3) m. K)/(\lambda max)` (1)

Where T is the effective temperature of the star.

Bodies that are hot enough emits light as consequence of its temperature. For example, a iron bar in contact with fire will start to change colors as the temperature increase, until it gets to a blue color, which its know as Wien's displacement law. Which establishes that the peak of emission for the spectrum will be displaced to shorter wavelengths as the temperature increase.

The same scenario described above can be found in the stars, a star whit higher temperature will have a blue color and one with lower temperature, a red color.

B.

Since star does not have the same size, they have different brightness, That is because the photons have a free mean path greater in a bigger radius.

So a star brightness is a consequence of its radius.

C.

Spectral lines will be shifted to the blue part of the spectrum1 if the source of the observed light is moving toward the observer, or to the red part of the spectrum when it is moving away from the observer (that is known as the Doppler effect).

By using that shift in the spectral lines, the Doppler velocity can be determined.

`v = c(\Delta \lambda)/(\lambda_(0))` (2)

Where
`\Delta \lambda` is the wavelength shift,
`\lambda_(0)` is the wavelength at rest, v is the velocity of the source and c is the speed of light.

D.

When a photon is absorbed by an electron in an atom of a particular element in the star photosphere, the electron will be pass to a higher state, when it comes back to the ground state, a photon will be emitted again. If the emitted photon does not go in the same direction of the incident photon an absorption line will be created in the spectrum of the star.

This patterns of spectral lines in the spectrum of the star are compared with the patterns that are got by lamps of that element in a laboratory.

Key term:

¹Spectrum: decomposition of light in its characteristic colors (wavelengths).