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
B
2.0g
C
1.6g
D
0.5g

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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