Question

the initial amount of carbon 14 is 100g and the amount of carbon 14 dropped to 1 g after decay process.the half line of carbon 14 is 5,730 y.calculate the time taken to complete this decay process​

Answer 1

Given info : the initial amount of carbon 14 is 100g and the amount of carbon 14 dropped to 1 g after decay process and the half line of carbon 14 is 5,730 yrs.

To find : The time taken to complete this decay process is ...

solution : using half life equation, T½ = ln2/k

where k is decay constant

given half life, T½ = 5730 yrs

so 5730 = ln2/k

⇒k = ln2/5730 ....(1)

initial amount of carbon 14, N₀ = 100g

final amount of it, N = 1g

using decay equation, N = N₀e^(-kt)

⇒1 = 100 × e^(-kt)

⇒ln(1/100) = -kt

⇒ln(100) = kt

⇒t = ln(100)/{ln2/5730} = 5730 × ln(100)/ln2

= 38069.3 yrs

Therefore the time taken to complete the decay process is 38069.3 yrs