If an isotope has a cycle (half-life) of 2,000 years, approximately what percent of an original amount will remain after 6,000 years

Question

asked Nov 7, 2024 219k views

1 Answer

BTMPL · Answer 1 · 2024-11-14T17:08:02+0000

Answer: 12.5%

Explanation:

Formula for Half Life

N = N₀
$((1)/(2) ^{(t)/(t_(1/2) ) } )$

N = number of isotopes after

N₀ = Initial Isotopes

t = number of years

t_(1/2) = half life years

Given

t=6000

t_(1/2) = 2000

Percent is part out of the whole = remaining/starting amoung

Percent fraction =
(N)/(N_(0) )

$(N)/(N_(0) ) = (1)/(2) ^{(t)/(t_(1/2) ) }$

$(N)/(N_(0) ) = (1)/(2) ^{(6000)/(2000 ) }$

(N)/(N_(0) ) = .125 =12.5%