Question #5d643

2 Answers
Jan 18, 2017

Answer:

4052 years old.

Explanation:

# 2^.5# = 1.414

25% is half of half life. so 2 to the .5 of a half life.

So the amount of the carbon left. is # 1/1,414 xx 5730# = 4052 years.

Feb 6, 2017

Answer:

The sample is 2380 years old.

Explanation:

We can express the rate law for a first-order decay as

#N_t/N_0 = (1/2)^n#

where

#N_t# is the amount remaining after time #t#.
#N_0# is the amount present at the start (#t = 0#).
#n# is the number of half-lives (#t_½#)

We can rewrite this as

#N_0/N_t = 2^n#

If the concentration of carbon-14 has decreased by 25 %, then 75 % remains.

#100/75 = 2^n#

#ln(100/75) = nln2#

#n = 0.2877/ln2 = 0.4150#

The sample has decayed for 0.4150 half-lives.

#0.4150t_½ = "0.4150 × 5730 yr" = "2380 yr"#