The half-life of Radium-226 is 1590 years. If a sample contains 500 mg, how many mg will remain after 2000 years?

Answer 1

A = 500(0.5)^2000/1590

A = 500(0.5)^1.257861635

A ≈ 500(0.418163303)

A ≈ 209.0816515

Answer 2

half life = 1590 yrs

total mass of sample Radium -226 = m = 500mg = 0.500g

after 1 half life remained sample i.e 1590 yrs = 250 mg

after 2000 yrs =

1 period = 1590 yrs

n = 2000 / 1590

= 1.26

a_n = a_o (1/2)ⁿ a_n is mass of remaining sample , a_o is mass of actual or original sample

= 0.500 (1/2)^1.26

^{= 0.208 g or 208 mg}