A radioactive element reduces to 25% of its initial mass in 1000 yrs .Find its half life
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half life of given radioactive element is 500 yrs.
A radioactive element reduces to 25% of its initial mass in 1000 yrs.
if N is initial amount of radioactive element
then, N_f = 25% of N = 0.25 N
using formula, t = 1/k ln[N/N_f]
1000 yrs = 1/k ln[N/0.25N]
= 1/k ln(4)
1000 yrs = 2ln2/k
⇒500 = ln2/k ........(1)
half life for radioactive element , T½ = ln2/k
from equation (1) we get,
T½ = 500 yrs
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