(A) The correct option is $A$. For a first-order reaction,the half-life period is given by the formula $t_{1/2} = \frac{\ln(2)}{k} = \frac{0.693}{k}$.

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Half-life period $= \text{constant} / k$,where $k$ is the decay constant

(A) The correct option is $A$. For a first-order reaction,the half-life period is given by the formula $t_{1/2} = \frac{\ln(2)}{k} = \frac{0.693}{k}$. Thus,$t_{1/2} = \text{constant} \times k^{-1}$.

Class 12 Chemistry Nuclear Chemistry Rate of decay and Half-life

Medium

The decay of a radioactive element follows first-order kinetics. As a result:

A
Half-life period $= \text{constant} / k$,where $k$ is the decay constant
B
Rate of decay is independent of temperature
C
Rate can be changed by changing chemical conditions
D
The element will be completely transformed into a new element after the expiry of two half-life periods

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Rate of decay and Half-life

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The decay of a radioactive element follows first-order kinetics. As a result:

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The ratio of $\frac{{}^{14}C}{{}^{12}C}$ in a piece of wood is $\frac{1}{8}$ part that of the atmosphere. If the half-life of ${}^{14}C$ is $5730 \text{ years}$,the age of the wood sample is $.....$ years.

The radium and uranium atoms in a sample of uranium mineral are in the ratio of $1 : 2.8 \times 10^6$. If the half-life period of radium is $1620$ years,the half-life period of uranium will be:

$A$ first-order nuclear reaction is half-completed in $45 \ minutes$. How long does it take for $99.9\%$ of the reaction to be completed in $hours$?

The half-lives of two radioactive nuclides $A$ and $B$ are $1 \ min$ and $2 \ min$ respectively. Equal weights of $A$ and $B$ are taken separately and allowed to disintegrate for $4 \ min$. What will be the ratio of weights of $A$ and $B$ disintegrated?

During a nuclear explosion,one of the products is $^{90}Sr$ with a half-life of $6.93 \; \text{years}$. If $1 \; \mu g$ of $^{90}Sr$ was absorbed in the bones of a newly born baby in place of $Ca$,how much time,in years,is required to reduce it by $90 \%$ if it is not lost metabolically?

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