Question

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

Answer 1

answer is c

Step-by-step explanation:

Answer 2

C) 10,500 years.

Step-by-step explanation:

• The decay of cobalt-60 is a first order reaction.

• The rate constant of the reaction (k) in a first order reaction = ln (2)/half-life = 0.693/(5272 year) = 1.314 x 10⁻⁴ year⁻¹.

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.