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Physics Question on deccay rate

The half-life of Ra226Ra ^{226} is 1620 years. Then the number of atoms decay in one second in 1g1 g of radium (Avogadro number =6.023×1023)\left.=6.023 \times 10^{23}\right)

A

4.23×1094.23 \times 10^{9}

B

3.16×10103.16 \times 10^{10}

C

3.61×10103.61 \times 10^{10}

D

2.16×10102.16 \times 10^{10}

Answer

3.61×10103.61 \times 10^{10}

Explanation

Solution

The number of atoms decay in one second
dNdt=λN\frac{d N}{d t} =\lambda N
=0.6931620×365×86×400×6.023×1023226=\frac{0.693}{1620 \times 365 \times 86 \times 400} \times \frac{6.023 \times 10^{23}}{226}
=3.61×1010=3.61 \times 10^{10}