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Physics-

General

Easy

Question

The half life of radium is 1620 years and its atomic weight is 226 kgm per kilomol. The number of atoms that will decay from its 1 gm sample per second will be (Avogadro's number $N equals 6.02 cross times 1 0 to the power of 26 end exponent$ atom/kilomol)

$3.61 \times 1 0^{10}$
$3.6 \times 1 0^{12}$
$3.11 \times 1 0^{15}$
$31.1 \times 1 0^{15}$

The correct answer is: $3.61 cross times 1 0 to the power of 10 end exponent$

$fraction numerator d N over denominator d t end fraction equals lambda N semicolon$ $lambda equals fraction numerator 0.6931 over denominator t subscript 12 end subscript end fraction equals fraction numerator 0.6931 over denominator 1620 cross times 365 cross times 24 cross times 60 cross times 60 end fraction comma$
$N equals fraction numerator 6.023 cross times 1 0 to the power of 23 end exponent over denominator 226 end fraction$
$therefore fraction numerator d N over denominator d t end fraction equals fraction numerator 0.6931 cross times 6.023 cross times 1 0 to the power of 23 end exponent over denominator 1620 cross times 365 cross times 24 cross times 60 cross times 60 cross times 226 end fraction$ = $3.61 cross times 10 to the power of 10 end exponent$

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