If the stars at the turnoff point in a star cluster have masses of about four solar masses, how old is the cluster

age of the cluster is 3.125 × 10⁸ years

Explanation:

Given that;

stars at the turnoff point in a star cluster have masses of about 4 solar masses

Age of the cluster?

we know that the main sequence lifetime of a star in solar lifetime(t) is related to the mass of the star in solar masses(M). expressed as

ζ = M^(-5/2)

our M is 4, so we substitute

ζ = 4^(-5/2)

ζ =  0.03125 solar lifetime

now convert the lifetime of star cluster into years

ζ = 0.03125 solar lifetime × (10¹⁰ years / 1 solar lifetime)

ζ = 312,500,000 ≈3.124 × 10⁸ years

therefore age of the cluster is 3.125 × 10⁸ years

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energy can be converted from one form to another, but it cannot be created or destroyed in ordinary chemical or physical means. do not understand what you are asking but hope this