The activity of a radioactive substance falls to 87.5 % of the initial value in 5 years. What is the half-life of the element ?

Question

The activity of a radioactive substance falls to 87.5 % of the initial value in 5 years. What is the half-life of the element ? (A)  52 years (B)  104 years (C)  26 years (D)  13 years

Tardigrade Admin · Accepted Answer

∵ λ = (2.303/t) log (N0/N) Here t= 5 years, N0 = 100, N = 87.5 ∴ λ = 0.0267 year-1 ∵ t12=(0.693/λ) = (0.693/0.0267) = 25.95 years ≈ 26 years

Q. The activity of a radioactive substance falls to $87.5%$ of the initial value in $5$ years. What is the half-life of the element ?

$52$ years

$104$ years

$26$ years

$13$ years

$∵ λ = \frac{2.303}{t} l o g \frac{N _{0}}{N}$
Here $t = 5$ years, $N_{0} = 100, N = 87.5$
$∴ λ = 0.0267$ year $^{- 1}$
$∵ t_{12} = \frac{0.693}{λ} = \frac{0.693}{0.0267} = 25.95$ years
$\approx 26$ years

Q. The activity of a radioactive substance falls to 87.5% of the initial value in 5 years. What is the half-life of the element ?

52 years

104 years

26 years

13 years