physics

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if 5/6th of a radioactive sample decay in 70 years and 1/6th remain. how can you find the half life without knowing the decay constant can you help?

• physics -

The fraction (1/6) that remains after 70 years satisfies the relation:

1/6 = 2^(-t/T),

where T is the half life and t = 70 years.

Take logs of both sides to solve for T. I'll use logs to base e but it doesn't matter

-1.7918 = -70/T ln 2 = -48.52/T
T = 27.1 years

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