The rate of radioactive disintegration at an instant for a radioactive same of half life 2.2 × 109 s-1 is 1010 s-1. The number of radioactive atoms in that sample at that instant is,

Question

The rate of radioactive disintegration at an instant for a radioactive same of half life 2.2 × 109 s-1 is 1010 s-1. The number of radioactive atoms in that sample at that instant is, (A) 3.17 × 1020 (B) 3.17 × 1017 (C) 3.17 × 1018 (D) 3.17 × 1019

Tardigrade Admin · Accepted Answer

T1/2 = 2.2 × 109 s, R = 1010 s-1 , R = Nλ N = (R/λ) = (R/0.693)T1/2 = (1010 × 2.2 × 109/0.693) = 3.17× 1019 atoms

Q. The rate of radioactive disintegration at an instant for a radioactive same of half life $2.2 \times 1 0^{9} s^{- 1}$ is $1 0^{10} s^{- 1}$ . The number of radioactive atoms in that sample at that instant is,

$3.17 \times 1 0^{20}$

$3.17 \times 1 0^{17}$

$3.17 \times 1 0^{18}$

$3.17 \times 1 0^{19}$

$T_{1/2} = 2.2 \times 1 0^{9} s, R = 1 0^{10} s^{- 1}, R = N λ$
$N = \frac{R}{λ} = \frac{R}{0.693} T_{1/2}$
$= \frac{1 0 ^{10} \times 2.2 \times 1 0 ^{9}}{0.693}$
$= 3.17 \times 1 0^{19}$ atoms

Q. The rate of radioactive disintegration at an instant for a radioactive same of half life 2.2×109s−1 is 1010s−1. The number of radioactive atoms in that sample at that instant is,

3.17×1020

3.17×1017

3.17×1018

3.17×1019