Question

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

Answer 1

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%