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General Chemistry

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Moderate

Rate Constant and Half Life of the Radioactive Substance

CHEM-ZYYRJE

A radioactive decay of a substance is as follows:

Time (days) Mass (g)
0 650
1 506.22
2 394.25
3 306.72
4 238.63
5 185.65

$\ $
What is the first-order decay constant and the half-life of the reaction?

Use the following formulas to answer the question:

$${ t }_{ 1/2 }=\cfrac { ln 2 }{ k } =\frac { 0.693 }{ k }$$

and

$$ln\cfrac { A_o }{ A } =kt$$

A

${ 1.00 \ \text{days} }^{ -1 } \ \text{and} \ 0.6927 \ \text{days}$

B

${ 0.75 \ \text{days} }^{ -1 } \ \text{and} \ 0.9237 \ \text{days}$

C

${ 0.25 \ \text{days} }^{ -1 } \ \text{and} \ 2.771 \ \text{days}$

D

${ 0.50 \ \text{days} }^{ -1 } \ \text{and} \ 1.386 \ \text{days}$