Question

living organisms have a 14 C decay rate of about .24 events/gram. if an ice man is discovered and found to have a decay rate of .06 events/gram how long ago did he die. (half life of 14 C is about 6,000 years)

Answer 1

Initially, there was No 14 C and the decay rate was dNo/dt
Using the equation of radioactive decay, dNo/dt = - No
Where is the decay constant. Given that dNo/dt = 0.24 events/gram
0.24 events/gram = - No         ...(1)

Later after time t, No decayed after N amount of 14 C was left.
dN/dt = - N
Given dN/dt = 0.06 events/gram
0.06 events/gram = - N            ...(2)
(1)/(2) gives
No/N = 0.24/0.06 = 4              ...(3)

N can be written as N = No e^-t             ...(4)
= 0.693/T_1/2 = 0.693/6000 year^-1.
= 1.155 x 10^-4 year^-1

From (3), No/N = e^t
Substituting (3),
4 = e^t
Taking ln on both the sides,
1.386 = t
t = 1.386/
= 1.386/(1.155 x 10^-4)
= 12002.55 years