A ancient discovery found a sample, where 75 % of the original carbon ( C ¹⁴ ) remains. Then the age of the sample is ( array r T_ 1 2 ( C ¹⁴ )=5730 years, 0.5=-0.7 (0.75)=-0.3 array )

Step-by-step solution

For a carbon sample ( C ¹⁴ ) , T_ 1 / 2 =5730 year Decay constant, K= 0.693 T_ 1 / 2 aligned & = 0.693 5730 & =1.209 10⁻⁴ / year aligned The rate of counts is proportional to the number of C ¹⁴ atom in the sample N₀=100, N=75 The age of the sample is given as, t= 2.303 K N₀ N = 2.303 K 1 0.75 aligned & = 2303 1.209 10⁻⁴ 100 75 & =2456 10^3 years & =2456 years aligned