A star's spectrum emits more radiation with a wavelength of 700.0 nm than with any other wavelen

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A star's spectrum emits more radiation with a wavelength of...

A star's spectrum emits more radiation with a wavelength of $700.0 \mathrm{nm}$ than with any other wavelength. (a) What is the surface temperature of the star? (b) If the star's radius is $7.20 \times 10^{8} \mathrm{m},$ what power does it radiate? (c) If the star is 9.78 ly from Earth, what will an Earth-based observer measure for this star's inten- sity? Stars are nearly perfect blackbodies. [Note: ly stands for light-years.]

A star's spectrum emits more radiation with a wavelength of $700.0 \mathrm{nm}$ than with any other wavelength.
(a) What is the surface temperature of the star? (b) If the star's radius is $7.20 \times 10^{8} \mathrm{m},$ what power does it radiate? (c) If the star is 9.78 ly from Earth, what will an Earth-based observer measure for this star's inten-
sity? Stars are nearly perfect blackbodies. [Note: ly stands for light-years.]

Key Concepts

Stefan-Boltzmann Law

The Stefan-Boltzmann Law states that the total power radiated per unit surface area of a blackbody is proportional to the fourth power of its temperature. When applied to a star, it allows for the calculation of the star's luminosity or total power output by considering its temperature and surface area.

Inverse Square Law

The Inverse Square Law describes how the intensity of radiation decreases with distance from a point source. For stars, it means that the observed brightness or intensity from Earth diminishes in proportion to the square of the distance between the star and the observer. This law is fundamental in converting a star’s luminosity into the intensity measured at a given distance, such as from Earth.

Blackbody Radiation

Blackbody radiation refers to the theoretical concept of an object that absorbs all incident electromagnetic radiation and then re-emits energy with a spectrum solely determined by its temperature. Stars are often approximated as blackbodies, meaning they emit a continuous spectrum that can be used to determine their physical properties such as temperature, luminosity, and power output.

Wien's Displacement Law

Wien's Displacement Law provides a direct relationship between the temperature of a blackbody and the wavelength at which it emits radiation most strongly. Specifically, the product of the peak wavelength and the temperature is a constant. This law is used to calculate the surface temperature of stars based on the observed wavelength of maximum emission.

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