Cobalt-60 can be used by scientists for the purpose of radioactive dating. cobalt-60 has a half-life of 5,272 years. a fossilized rock originally contained 25 grams of co-60. when tested, the rock only contains 6.25 grams of co-60. approximately how old is the item?

a) 2,600 years

b) 5,200 years

c) 10,500 years

d) 15,600 years
the correct answer is c

C) 10,500 years.

Explanation:

The integration law of a first order reaction is:

kt = ln [A₀]/[A]

k is the rate constant = 1.314 x 10⁻⁴ year⁻¹.

t is the time = ??? years.

[A₀] is the initial percentage of cobalt-60 = 25.0 g.

[A] is the remaining percentage of cobalt-60 = 6.25 g.

∵ kt = ln [Ao]/[A]

∴ (1.314 x 10⁻⁴ year⁻¹)(t) = ln (25.0 g)/(6.25 g)

(1.314 x 10⁻⁴ year⁻¹)(t) = 1.386.

∴ t = 1.386/(1.314 x 10⁻⁴ year⁻¹) =  10,550 years ≅ 10,500 years.

12 is it do you think so