What would the decay constant be ?

Question

A certain radioactive substance with a half- life of 2600 years is used in estimating the age of relics . Part 1: Find the decay constant. Give excat symbolic answer.

Answer 1

Relation between Half life and Decay Constant is

T = 0.693/ λ

Where T = Half life and λ = Decay constant

Given T = 2600 years

so λ = 0.693/T = 0.693 /2600 = 0.00026654 years ^-1 = 2.6654 *10^-4 years ^-1

Answer 2

e^-2600λ = 1/2

-2600λ = ln(1/2) = - ln(2)

λ = ln(2)/2600