Carbon-14 has a half-life of 5720 years and this is a first order reaction. If a piece of wood has converted 75% of the carbon-14, then how old is it?

A) 11440 years

B) 2375 years

C) 4750 years

D) 4290 years

E) 1430 years

Question

Mathematics

Emery Conrad

2 January, 05:13

Carbon-14 has a half-life of 5720 years and this is a first order reaction. If a piece of wood has converted 75% of the carbon-14, then how old is it?

A) 11440 years

B) 2375 years

C) 4750 years

D) 4290 years

E) 1430 years

+2

Answers (1)

Know the Answer?

Sylvia Christian · Answer 1

The amount of the substance (At) at any time t is calculated through the equation,

At = (A0) (e^-kt)

where A0 is the initial amount and k is constant.

For the half-life,

ln (At / A0) = ln 0.5 = - k (5270 years)

The value of k is 1.3153x10^-4 / year.

Substituting this value to the same equation, where At = 0.25A0

ln 0.25 = - (1.3153 x 10^-4) (t)

The value of t from this equation is 10540 years. The closest value to this is letter A.

Carbon-14 has a half-life of 5720 years and this is a first order reaction. If a piece of wood has converted 75% of the carbon-14, then how old is it?A) 11440 yearsB) 2375 yearsC) 4750 yearsD) 4290 yearsE) 1430 years

Carbon-14 has a half-life of 5720 years and this is a first order reaction. If a piece of wood has converted 75% of the carbon-14, then how old is it?

A) 11440 years

B) 2375 years

C) 4750 years

D) 4290 years

E) 1430 years