Question

If 87.5 percent of a sample of pure Thallum-99 decays in 24 days,what is the half-life of Thalium-99 ?

​

Answer 1

Answer:

it's like a, math question

Answer 2

Given info : If 87.5 % of a sample of pure Thallium -99 decays in 24 days.

To find : the half life of Thallium -99 is ..

solution : let N₀ is initial amount of Thallium -99

after 24 days, remaining amount of Thallium - 99 = N₀ - 87.5% of N₀

                                                                                  = N₀ - 7/8 N₀ = 1/8N₀

using formula, $N=N_0e^{-\lambda t}$

Here, N₀/8 = N₀$e^{-\lambda 24}$

⇒ 1/8 = $e^{-24\lambda}$

⇒ λ = ln(8)/24 = 3ln2/24 = ln2/8 ..(1)

now half life of radioactive decay, $t_{half}$ = ln2/λ

from equation (1) we get, $\bold{t_{half}}$ = ln2/(ln2/8) = 8 days

therefore the half life of Thallium -99 is 8 days.