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If a radioactive substance has a half-life of 4,500 years, how much of an initial mass of 100g will be left after 20,000 years? And what is the constant of decay of this substance? Thank you for help.

Guest Sep 10, 2018

#1**0 **

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Guest Sep 10, 2018

edited by
Guest
Sep 10, 2018

edited by Guest Sep 10, 2018

edited by Guest Sep 10, 2018

edited by Guest Sep 10, 2018

edited by Guest Sep 10, 2018

#2**0 **

A = A(0) * 1/2^(20,000/4,500)

A = 100 * 1/2 ^4.44.....

A =100 x 4.59....

**A =~4.59g remaining after 20,000 years.**

k = -(ln2) / half-life

k =- (0.693147) / 4,500

**k = -0.000154 - which is the constant of decay.**

Check: A =100 x e^-(0.000154*20,000)

A =100 x e^ -3.08

A =100 x 0.0459.....

A =4.59 grams.

Guest Sep 10, 2018