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## The mass luminosity relation L M 3.5 describes the mathematical relationship between luminosity and mass for main sequence stars. It descr

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The mass luminosity relation L M 3.5 describes the mathematical relationship between luminosity and mass for main sequence stars. It describes how a star with a mass of 2 M⊙ would have a luminosity of _____________ L⊙ while a star with luminosity of 3,160 L⊙ would have an approximate mass of ________________ M⊙.

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6 months
2021-08-22T05:50:11+00:00
2021-08-22T05:50:11+00:00 1 Answers
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## Answers ( )

Answer:(a)

11.3 L(b)

10 MExplanation:The mass-luminosity relationship states that:

Luminosity ∝ Mass^3.5Luminosity = (Constant)(Mass)^3.5So, in order to find the values of luminosity or mass of different stars, we take the luminosity or mass of sun as reference. Therefore, write the equation for a star and Sun, and divide them to get:

Luminosity of a star/L = (Mass of Star/M)^3.5 ______ eqn(1)where,

L = Luminosity of Sun

M = mass of Sun

(a)It is given that:

Mass of Star = 2M

Therefore, eqn (1) implies that:

Luminosity of star/L = (2M/M)^3.5Luminosity of Star = (2)^3.5 LLuminosity of Star = 11.3 L(b)It is given that:

Luminosity of star = 3160 L

Therefore, eqn (1) implies that:

3160L/L = (Mass of Star/M)^3.5taking ln on both sides:

ln (3160) = 3.5 ln(Mass of Star/M)8.0583/3.5 = ln(Mass of Star/M)Mass of Star/M = e^2.302Mass of Star = 10 M