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Vitek1552 [10]
3 years ago
11

The mass luminosity relation L  M 3.5 describes the mathematical relationship between luminosity and mass for main sequence sta

rs. 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⊙.
Physics
1 answer:
ivanzaharov [21]3 years ago
3 0

Answer:

(a) <u>11.3 L</u>

(b) <u>10 M</u>

Explanation:

The mass-luminosity relationship states that:

Luminosity ∝ Mass^3.5

Luminosity = (Constant)(Mass)^3.5

So, 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)^3.5

Luminosity of Star = (2)^3.5 L

<u>Luminosity of Star =  11.3 L</u>

(b)

It is given that:

Luminosity of star = 3160 L

Therefore, eqn (1) implies that:

3160L/L = (Mass of Star/M)^3.5

taking 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^2.302

<u>Mass of Star = 10 M</u>

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