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Question

The half-life of Pa-218 is 3 minutes. What mass of a 16g sample of Pa-218 will remain after 15 minutes?


A
3.2g
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B
2.0g
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C
1.6g
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D
0.5g
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Solution

The correct option is B 0.5g

$$t_{1/2}= 3 \ minutes$$

$$K= \cfrac {2.303}t \ log \ \cfrac {A_o}{A}$$

Also, $$t_{1/2}= \cfrac {0.693}{K}$$

$$\Rightarrow K= \cfrac {0.693}3 = 0.231$$

After $$15 \ minutes$$

$$K= \cfrac {2.303}{15} \ log \ \cfrac {15}{x}$$

$$\Rightarrow 0.231 = \cfrac {2.303}{15} \ log \cfrac {15}{x}$$

$$\Rightarrow \boxed {x=0.5 \ g}$$ [Remaining concentration]


Chemistry

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