The half life of a radioactive material is 24 hours. The time taken for the radioactive material to decay to ((1/8))th of its initial amount is

Question

The half life of a radioactive material is 24 hours. The time taken for the radioactive material to decay to ((1/8))th of its initial amount is (A) 72 hours (B) 24 hours (C) 96 hours (D) 48 hours

Tardigrade Admin · Accepted Answer

(N/N0)=((1/2))n where, n = number of half lives ∴ (1/8)=((1/2))n ⇒ n=3 ∵ n=(t/T1 /2) ∵ t=n T1 /2=3×24 hours =72 hours

Q. The half life of a radioactive material is $24$ hours. The time taken for the radioactive material to decay to $(\frac{1}{8})^{t h}$ of its initial amount is

$72$ hours

$24$ hours

$96$ hours

$48$ hours

$\frac{N}{N _{0}} = (\frac{1}{2})^{n}$
where, $n =$ number of half lives
$∴ \frac{1}{8} = (\frac{1}{2})^{n}$
$\Rightarrow n = 3$
$∵ n = \frac{t}{T _{1/2}}$
$∵ t = n T_{1/2} = 3 \times 24$ hours
$= 72$ hours

Q. The half life of a radioactive material is 24 hours. The time taken for the radioactive material to decay to (81​)th of its initial amount is

72 hours

24 hours

96 hours

48 hours