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Standard XII

Chemistry

Planck's Quantum Hypothesis

What mass of ...

Question

What mass of $^{14} C$ with $T_{50 %} = 5730$ years has activity equal to one curie?

0.2244 g

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0.4244 g

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0.3244 g

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0.6729 g

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Solution

The correct option is C $0.2244 g$
$1 C i = 3.7 \times 10^{10} d p s$
$t_{50} = 5730 y e a r s = 5730 \times 3.1536 \times 10^{7} s$
$∴ λ = \frac{0.693}{t_{50}} = \frac{0.693}{5730 \times 3.1536 \times 10^{7}} s^{- 1}$
$- \frac{d N}{d t} = λ N = \frac{λ w \times 6.02 \times 10^{23}}{14}$
$3.7 \times 10^{10} = \frac{0.693 \times w \times 6.02 \times 10^{23}}{5730 \times 3.1536 \times 10^{7} \times 14}$
$w = 0.2244 g$

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Similar questions

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What mass of 14C with T50%=5730 years has activity equal to one curie?

The correct option is C 0.2244g1Ci=3.7×1010dpst50=5730years=5730×3.1536×107s∴λ=0.693t50=0.6935730×3.1536×107s−1−dNdt=λN=λw×6.02×1023143.7×1010=0.693×w×6.02×10235730×3.1536×107×14w=0.2244 g

What mass of $^{14} C$ with $T_{50 %} = 5730$ years has activity equal to one curie?