the isotope 146c has a half life of 5730 years. what fraction of 146c in a sample with mass ,m, after 28650 years

3.1% is the fraction of the sample after 28650 years

Explanation:

The isotope decay follows the equation:

Ln[A] = -kt + Ln[A]₀

Where [A] could be taken as fraction of isotope after time t, k is decay constant and [A]₀ is initial fraction of the isotope = 1

k could be obtained from Half-Life as follows:

K = Ln 2 / Half-life

K = ln 2 / 5730 years

K = 1.2097x10⁻⁴ years⁻¹

Replacing in isotope decay equation:

Ln[A] = -1.2097x10⁻⁴ years⁻¹*28650 years + Ln[1]

Ln[A] = -3.4657

[A] = 0.0313 =

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