Answer :

The wavelength of the line on star C-197's spectrum is 517.88. A spectrum is a range of electromagnetic radiation, such as light, that is divided into separate bands based on wavelength.

Using the formulae :-

Wavelength (λ) = Speed of light (c) ÷ frequency (f).

Therefore, 517.88 = 3 x 10^8 / f,

and f = 3 x 10^8 / 517.88

= 5.81 x 10^14

The wavelength of a spectral line can be used to identify the chemical elements present in a star and to determine its temperature, density, and other physical characteristics. The wavelength of a spectral line is the distance between two consecutive peaks (or troughs) of a wave. In the case of a star's spectrum, the wavelength of a spectral line is the distance between two consecutive peaks (or troughs) in the light emitted by the star. The specific wavelength of a spectral line is unique to a particular chemical element and is characteristic of that element. To determine the wavelength of a line on a star's spectrum, the spectrum must be observed and analyzed using a spectrometer. The spectrometer splits the light from the star into its component colors and records the intensity of light at each wavelength. The resulting spectrum is a graph of the intensity of light at each wavelength. The spectral lines are the spikes in intensity that correspond to light emitted at specific wavelengths by specific chemical elements. The wavelength of a particular line on a star's spectrum can be measured by finding the position of the peak in intensity corresponding to that line and recording its wavelength.

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Final answer:

To find the wavelength of a spectral line from star C-197's spectrum, the observed wavelength shift must be measured and compared to the known rest wavelength. The velocity of the object can then be calculated using the Doppler effect formula involving the observed and rest wavelengths of the spectral line.

Explanation:

The question pertains to the Doppler effect on the spectral lines of a distant object in space, which is typically studied in the field of astrophysics, a branch of physics. When analyzing spectral lines, you can determine the relative velocity of a star or galaxy with respect to Earth by measuring the shift in wavelengths of known spectral lines. This is known as the redshift for wavelengths longer than the rest wavelength (moving away) or blueshift for wavelengths shorter than the rest wavelength (moving towards).

In the case of star C-197, to determine the wavelength of the spectral line from its spectrum, you would need specific data about the observed wavelength shift. Once you have the observed wavelength, you can compare it to the known rest wavelength of the spectral line in question. If star C-197's spectrum is not provided, we can't calculate the exact wavelength; however, for the examples given such as the galaxy associated with 3C 273, the redshift was so significant that its spectral lines from the Balmer series (normally in the visible range) were shifted into the infrared range due to its high velocity away from Earth.

To calculate the velocity of a star or galaxy moving relative to Earth, the formula used involves the observed wavelength (λobserved), the rest wavelength (λrest), and the speed of light (c). The formula is:

  • v = c * ( λobserved - λrest ) / λrest

For instance, if an emission line of hydrogen is normally at 656.3 nm and observed at 656.6 nm, you can calculate the velocity of the source using the formula above.