After 30 days, 5.0 grams of a radioactive isotope remains from an original 40.-gram sample. what is the half-life of this element?

M₀ = 40 g, original mass
m₁ = 5.0 g, mass remaining after 30 days.

The decay equation is of the form

where
t = time, days
k = constant

Therefore


At half-life, m = 20 g.
The time for half-life is


10 days

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