The half-life of Ra 226 is 1620 years. Then the number of atoms decay in one second in 1 g of radium (Avogadro number .=6.023 × 1023)

Question

The half-life of Ra 226 is 1620 years. Then the number of atoms decay in one second in 1 g of radium (Avogadro number .=6.023 × 1023) (A) 4.23 × 109 (B) 3.16 × 1010 (C) 3.61 × 1010 (D) 2.16 × 1010

Tardigrade Admin · Accepted Answer

The number of atoms decay in one second (d N/d t) =λ N =(0.693/1620 × 365 × 86 × 400) × (6.023 × 1023/226) =3.61 × 1010

Q. The half-life of $R a^{226}$ is 1620 years. Then the number of atoms decay in one second in $1 g$ of radium (Avogadro number $= 6.023 \times 1 0^{23})$

$4.23 \times 1 0^{9}$

$3.16 \times 1 0^{10}$

$3.61 \times 1 0^{10}$

$2.16 \times 1 0^{10}$

The number of atoms decay in one second
$\frac{d N}{d t} = λ N$
$= \frac{0.693}{1620 \times 365 \times 86 \times 400} \times \frac{6.023 \times 1 0 ^{23}}{226}$
$= 3.61 \times 1 0^{10}$

Q. The half-life of Ra226 is 1620 years. Then the number of atoms decay in one second in 1g of radium (Avogadro number =6.023×1023)

4.23×109

3.16×1010

3.61×1010

2.16×1010